This is a factual question, but factual questions about election-related stuff keep… evolving… into debate questions so I’m pre-emptively putting it here. 
I have assumed that there are actual laws either directly against profiting from the office, or else aimed at preventing a president from being able to do so. But some remarks I’ve read here and there are making me wonder whether in fact it’s not actually illegal, just unethical.
What’s the facts?
I honestly don’t know, but I’m having a hard to imagining how the president could be arrested for anything. One thing’s for sure, the prez can only be removed from office by first being impeached (per the Constitution). If he were arrested and not impeached, he’d still be the president.
If the president shot a random passerby in plain view in Times Square, what would prevent him from getting arrested?
Certainly enrichment via bribery and influence peddling can bring a president down. Agnew - VP working under the same laws - had to resign for such.
But a President who takes an endorsement deal to wear Rolexs or something? I honestly don’t know.
If there is one silver lining to Trump’s rise to power (the part of my brain still in denial about the election had a hard time letting me type this clause, btw), its that it may prompt reactive legislation to address what clearly is a longstanding policy gap. That we haven’t even really probed these questions until now is kind of scary on one hand. On the other hand, it just highlights how different Trump is from all his predecessors. While it could be speculated that others had conflicts of interests, we know Trump does. So it’s not a question of “if”. It’s two questions: “What can be done about it?” and “Why hasn’t Marty gone back to 1955 and fixed this shit yet?”
What continues to amaze me about the Trumps is that they hide nothing. The guy isn’t even sworn in yet and he’s got his daughter in meeting with heads of state.
The Secret Service, charged with assuring the safety and security of the sitting president, would prevent him from being arrested. It would be foolish for a municipal or state law enforcement agent to try, and there are any number of provisions by which federal law enforcement agencies (including the Secret Service, Federal Bureau of Investigation, Federal Marshals Service, Department of Defense Policies, et cetera, could claim jurisdiction, take the over custody of the president, and then release him or her.
Although there is Constitutional protection of the Office of the President of the United States from being removed from authority, there is, perhaps surprisingly, no special protection of the president as an individual under the Constitution or United States Code against arrest or prosecution of crimes while in office, but there is a tradition and supporting opinions in various Federalist Papers and elsewhere that a sitting president should be able to operate freely without threat of arrest until he or she leaves office. The president can only be removed from office by the process of impeachment by the House of Representatives and conviction by the Senate for “high crimes and misdemeanors”, a standard that is vague enough to have been interpreted as perjury and obstruction of justice for lying under oath about consensual extramarital sex. (Bill Clinton was impeached by the House but not convicted by the Senate on a vote that was mostly along party lines despite the essential facts of the case not being in dispute, presumably on the basis that getting a blowjob from an intern is not a "high crime or misdemeanor, which is probably a good thing because we’d have to reflect on the many former presidents who should have been impeached and were not.)
The president is not technically immune from civil suits, and in fact is frequently the target of such suits for various reasons (the investigation and impeachment of Bill Clinton started in part in response to a harassment suit by Paula Jones), but generally speaking may be given special consideration in being compelled to testify in deference to the requirements of the Presidential Office, e.g. a suit being deferred until leaving office, giving testimony by pre-recorded video, dismissal for being judged as politically motivated, et cetera. The president is not immune from violation of criminal statutes, hence why the incoming President Ford pardoned the outgoing President Nixon, but there is a rational argument for why a sitting president should not have to respond to local or state law enforcement lest he or she be hamstrung by politicallly motivated prosecution by unelected officials or agents who were only elected by a small segment of the population.
Bribery, graft, theft, extortion, racketeering, direct solicitation of money or real estate in exchange for services or influence, use of executive authority to intentionally violate individual rights, and conspiracy with others to do the same or conceal illegal activities before, during, and after the fact are all illegal and covered by federal statutes (Hobbs Act, Travel Act, RICO, Foreign Corrupt Practices Act, mail and wire fraud provisions of interstate commerce laws, Federal Acquisition Regulations, et cetera), which is intended to prevent the officials including the president from just taking money or using influence of the Office of the President to enrich himself or otherwise commit illegal acts against the public interest.
However, short of openly committing a “high crime or misdemeanor” there is little that the president actually can’t do within the scope of Constitutional authority (as spelled out in Article 2 of the US Constitution), including issuing executive orders which direct action in violation of statute law or suspending such law, or making executive agreements with foreign governments and non-governmental actors (although to received funding or be instituted as treaty obligations they typically have to be ratified by the legislature). Such orders can only be contested by Federal court challenge or impeachment. The president can also invoke executive privilege and state secrets privilege to avoid disclosure of actions and orders, effectively shielding himself or herself from normal judicial review of executive decisions unless there is reason to believe that the actions were overtly criminal. About the only thing the president cannot do within the bounds of executive authority is simultaneously hold office and also be a member of the legislature or judiciary, introduce legislation, or dismiss members of the legislature, judiciary, or officials appointed by Senate confirmation.
The expectation is that a president will not use the enormous power entrusted in the office for personal enrichment, intentional violation of Constitutional protections, or to deliberate attack individuals for personal or partisan reasons, which is an assumption that we may be rethinking pretty shortly. There is certainly nothing preventing the president from holding a second job, having an outside stream of income, investing or owning companies or interests that may benefit from executive decisions and actions, or using executive authority to favor future interests. Although the president and cabinet members have traditionally put companies in which they have a controlling or significant interest or major assets into a blind trust managed by a supposedly impartial agent entrusted to oversee the trust without direction or regular communication with the owner, there is no Constitutional or legal requirement to do so
Here is a position paper from the Yale Law School Legal Scholarship Repository that briefly discusses the various pertinent Constitutional provisions and decisions, opining “Apart from these points about history and tradition, my basic constitutional argument is more structural than textual, sounding in both separation of powers and federalism,” i.e. the separation of financial and personal conflicts of interest is more about a tradition of integrity and respect for the office in order to permit the president to operate without undue restraint than any legal strictures, which is again something we may be reconsidering in the near future.
Stranger
Blame the liberals’ yuckily sentimental ‘Bring Your Daughter To Work Day’.
As for Trump, Let a Thousand Infomercials Bloom ! 'As Endorsed By the President of the United States !
There is very little that could be done in a purely legislative context to limit the scope of powers of the president because those powers are either specifically delineated by the Constitution, Article 2, or have been recognized by precedent and judicial opinion, witness the Line Item Veto act or provisions of the Patriot Act that were struck down despite legislative support. Contracting presidential executive authority would have to be done either by legal challenge in front of the Supreme Court or by amendment of the Constition. Trump, of course, will likely appoint several lower federal court and Supreme Court justices who will favor expanded executive authority (and as much as Republicans have bitched about this for the past eight years they’ll certainly support a nomination of a candidate that otherwise is in agreement with their political bent), and getting the necessary 38 states to ratify an amendment, while not impossible, would be the work of years of garnering support and likely backroom wheeling and dealing that might be just as bad, even supposing you could get the legislature to vote it through. And frankly, this isn’t some kind of policy gap; the Office of the President was endowed with this authority for specific reasons (to allow the US to have a strong executive face to the world, deal with internal strife and international conflict decisively, inhibit political factioning from making the president a rubber stamp, et cetera). The executive authority of the office has grown stronger over the years to be sure, but that was largely in response to the more prominent position and influence the United States has had in world affairs and growth of the country with often conflicting and divisive interests. The Constitutional and federal election law have not failed; it is the electorate which has failed to make sensible choices, in large measure fueled by the believe that the US is an inherently two party system, both of which have become so polarized and stagnant that they no longer reflect the broad spectrum of social and political thought in the country and selected candidates that more people voted against than for.
Arguably the office should be even stronger that it is (e.g. the afformentioned line item veto) in the face of economic volatility and social unrest that is beyond legislative action to effectively address. However, this assumes that informed and benevolent individuals focused on broad address of socioeconomic injustice, reform of outmoded or corrupt institutions, and selfless service to the nation would occupy and advise the office. The last time we actually had anything like that across the board was arguably Jimmy Carter, and the sheer ineffectness of his administration shows just how little we can expect in what is probably the best case.
The president is essentially free to pick whomever he wants to advise him and represent his interests. One might equally rail against Kennedy who relied heavily on his father-in-law and brother to recommend members of his cabinet. The galling thing about Trump isn’t that he’ll use the office to enrich himself or the fawning nepotism that is sure to inform his tenure, but that he has selected unqualified extremist wackjobs for vital advisory and executive positions of his transition team and presidential appointments. So far we have an open racist, a conspiracy nutter, a hyperconservative talk show host, and a climate change denier unversed in science or statistics to strategic positions. If “character is destiny” and Trump uses his advisors to shield himself from the reality of the tedious and frustrating minutiae of the job of president as he seems to want to do, we can only expect compulsively destructive, repressive, counterfactual executive action over the next four years, or at least as long as Trump decides to remain in office and the legislature deigns to indulge him to their own ends. We can just hope that he does not use aspects of executive authority such as his unchecked control of the nuclear arsenal and command of the military to do take action that the nation can never walk back from. At this point, the conrolling party appears to be unfazed by the amount of corruption being set in motion. Hopefully their voters will see past the fear and insecurity that led to the election of Trump and will join in non-partisan agreement to pressure them to do the best for the nation despite politics and mitigate the worst of the collateral damage that is about to unfold.
Stranger
President Grant was arrested while in office. For speeding (which was a crime even before cars). He was taken to a police station, paid his fine, and was released. So a President is legally subject to arrest.
What happens if Jed Bartlett gets annoyed at Toby Ziegler’s snide attitude and strangles him to death with his own necktie? The President gets arrested for murder and taken into custody. I would assume the cabinet would then gather together and declare “that the President is unable to discharge the powers and duties of his office” under the terms of the 25th Amendment and the VP becomes the Acting President. Congress can then make this more permanent by impeaching the President.
I don’t think that’s exactly right. They hide plenty. We still know almost nothing about his taxes since he, alone among all candidates, refuses to release his returns. We know even less about his finances. The true extent of the Trump University fraud will never come to light because the plaintiffs were bought out in a cash settlement. The incriminating Access Hollywood tape was met with staunch denial that he ever actually did any of those things. The women who said he did were openly called liars and threatened with lawsuits.
What is true is that Trump is shameless and brazen about things that can’t be hidden, many of which – like racism, Islamophobia, and general xenophobia – are actually celebrated and promoted.
ETA: And in reference to the OP, I suspect there is going to be more self-enrichment and abuse of power in this administration than in any other in modern history. How much of it will come to light is anybody’s guess. Trump has never – ever – missed an opportunity to make a buck or a million or three, and ethics is not his strong point.
That’s kind of understatement in the same way that saying, “Albert Einstein kind of changed the course of physics,” or “Pol Pot might have been responsible for a few deaths.”
And while we don’t really have a comparable example in our history (in this Trump will the best, absolute best, much bigger than Harding), we can look elsewhere for examples of what a Trump presidency might look like.
Stranger
When i moused-over and saw that the link was to YouTube, I was expecting this. If you think this country’s bad off now, just wait 'til Trump gets through with it.
But I think Matt Yglesias draws a pretty good parallel - to Silvio Berlusconi. And I think Yglesias has a point: Trump really doesn’t have an ideology. There’s people who submit to him, and there are enemies. It’s easy to envision an America where those who kiss up to Trump are treated kindly by the apparatus of government, and those who don’t, not so kindly.
That was pre-Secret Service presidential protection.
I just know he would agree! 
A statement like “ethics is not his strong point” was of course intentionally sarcastic. Trump would rob his own mother and leave her on the street homeless for the price of enough gold paint to gild another tasteless chintzy faux-Louis XIV armchair in his tasteless chintzy gilded apartment.
That clip did miss the song about the new rules of the Rufus T Firefly’s administration.
[QUOTE] I will not stand for anything that's crooked or unfair I'm strictly on the up-and-up, so everyone beware If any man's caught taking graft, and I don't get my share We stand him up against the wall and pop! Goes the weasel [/QUOTE]Yep, sounds like Trump.