Voltaire said it best:
With great power comes great responsibility.
All right, uncle. Rules is rules. I’m not going to follow them anyway, but the OP’s question is answered.
ETA: I gues the ‘with’ on the beginning screws it up. Would you consider “Your promotion comes with new challenges and responsibilities” to be correct?
When I was in grade school, I had a book that starred a mythical creature called the “Churkendoose.”
(Amazon.com)
The Churkendoose was fond of saying, “It all depends on how you look at it.” This OP is a perfect example of that. The sentence makes sense either way, and thus both possibilities are equally correct.
“It all depends on how you look at it.”
Well, true rules of grammar are innate to the language but no native speaker, however much they text will violate those. Rules of usage are by convention, so, in that sense they’re meaningless, however continuity is important for universality and when people ask about the correct way to phrase something, generally, what they want is the historically appropriate method of phrasing it.
And I’m surprised and saddened at the number of people who have forgotten how to recognize an object of a preposition and how it should be treated when it comes to inflecting verbs. This is middle-school level stuff here, guys.
I agree with Wheelz’s opinion of this, and would add that how hard you have to work to understand the person that’s trying to communicate counts for something too.
Yes, but the two sentences are saying different things. The meat of the idea of your sentence is “Your promotion comes.” while the meat of the OP’s sentence is “New challenges and responsibilities come.” In this instance the difference is slight but it is a shift in focus.
Of course it’s correct, it’s perfectly grammatical.
If you’re not going to follow grammatical rules and do not care about knowing them, why are you replying in a thread asking about grammatical correctness?
“The steak comes with a salad and baked potato.”
“A salad and baked potato come with the steak.”
It all depends on how you look at it.
I must say I’m surprised that a native speaker of English would need to ask which is correct. Out of the two sentences in the OP, one immediately “feels” right and the other feels wrong, due to the obvious mismatch between subject and verb. And I was never taught prescriptive grammar rules.
I’m even more amazed that anyone would argue that “comes” is correct. Would they also say “Alice visit Bob and Carol”, because “Bob and Carol” are plural? 
Because if you build it…
Actually this argument is favoured by many respected linguists. It’s the classic prescriptivist versus descriptivist debate. Language changes and evolves over time. I think you’ll find that ‘leetspeak’ is the exact opposite of what s0meguy said. The clue is in the term ‘elite’, meaning exclusive. It’s not meant to be understood by all. Good grammar, punctuation etc assists in communicating clearly, but let’s not get bogged down in details.
Grammarians today do not set rules that people must abide by, they study how sentences are being constructed in a grammatical manner by the people using the language.
I think the lesson from this thread is, you either have an innate feel for language or you don’t. If you don’t, grammatical errors don’t leap out and annoy you, so you don’t care about them. 
“With your new promotion comes new challenges and responsibilities” just sounds horrible and grating, as the “comes” clashes with the plural subject. It’s like hearing “I washes the dishes” or something.
Well, I just read a comment on the NPR website where someone explained to me that came and went are for people and come and gone are for things. So I have no idea what english teachers are doing anymore because they can’t even churn out traditional prescriptivists.
Well, to be fair it does leap out - both sentences “feel” wrong. Which is why it should be re-written so you don’t have the proximate noun mismatching the plurality of the verb.
“New challenges and responsibilities come with your promotion” sounds better and has none of the ambiguity of the original. Or if you want to focus on the promotion: “Your promotion comes with new challenges and responsibilities”.
Where did I say I didn’t care about knowing them? It’s more difficult to break rules if you don’t know what they are, you can easily end up following them by accident. You should concentrate more on comprehension than syntax.
Prose ear. If you read a lot of traditionally edited materials, you gain a feel for how traditionally edited or ‘correct’ english should sound without necessarily being able to explain why.
The shift in focus may be something. But the relationship described is one to one. The literal meaning doesn’t change, and I don’t see an unambiguous shift in implication.
They’re saying that the preposition is significant in the structure of that sentence, and they seem to be backing it up. It doesn’t sound natural to me, but the OP does appear to be asking about the grammatical rules, not what feels right.
No, that’s bullshit. Did you see me do any of those things? A proponent of that argument?
In fact, I’d say that proponents of your argument are being intellectually lazy, for not thinking it through and instead going for what makes you feel superior.
Just because a word or grammatical rule isn’t officially recognized, does not mean it is wrong.
To illustrate my point, imagine this:
- A person starts using “there” instead of “their”.
- The group this person is in starts using “there” instead of “their”.
- The group creates a dictionary in which they redefine “there” as having the same meaning as “their”.
- The group creates a new country and creates a governmental institution that officially proclaims that “there” has the same meaning as “their” in that country.
Alternate story:
- The use of those words in that way expands to an entire existing country. The dictionary is changed to reflect the new meaning of the words.
So, where along the line did it become correct?
If you’re going to say nowhere, then keep in mind that many words of all non-constructed languages were formed/mutated this way. Also, once upon a time, there was no official institution to declare what is the right thing to say and what isn’t. So, what defines which word is the right one in that case? Have all words been “wrong” once? (when they were first made up by someone).
I haven’t heard that expression before, but I agree. As I said above, my English education was far from prescriptive (English comprehensive school in the 1980s), but I read a lot, so misspellings and grammatical errors leap out at me. That’s just as well, considering I now work as an editor. 