You want to ridicule him in front of onlookers by causing him to speak with a squeaky voice? You fiend!!!
As to myself, I would like to go to the early 17th century and try to convince the Spanish Hapsburg king that getting married with his cousin who is also his niece and somehow both his aunt and his grandmother twice removed is not at all conducive to offspring that looks even remotely human. Let’s see if I cannot get the Spanish Hapsburg dynasty to survive to modern times…!
I’d kidnap Helen of Troy myself, and make the whole Trojan War the result of a framing.
If it didn’t work for Cassandra, why would you have any better of a chance?
I’d blind Paul the Apostle a second time, then give him scabies.
Steal the original letter and substitute “Of course he doesn’t, you little twit! It’s your parents.”
I’d convince some Vikings to sail up the St. Lawrence and across the Great Lakes and leave a runestone in Minnesota with some spelling and grammatical errors. I’d drop crystal skulls off in various parts of the world. I’d show Easter Islanders how to wobble walk giant statues down to the beach. I’d go to Baghdad and leave some clay jars with a copper liner and a piece of iron in them. Stuff like that.
I’d take several crates of condoms with me and introduce the parents of multiple historical figures to the benefits of contraception. “Good morning, Mrs. Booth! May I interest you in a new and exciting product today?”
I’d make Hitler a high talker (like in the Seinfeld episode), with a VERY pronounced lisp.
Hmmm…two things come to mind
Go get John Wilkes Booth drunk on the evening of 04/15/1865.
Take a whole bunch of modern rifles and several thousand rounds of ammo to Travis at the Alamo.
For fun and mischief…?
During the premiere of Beethoven’s 9th symphony, slowly release helium gas about the choir as the 4th movement starts. By the time the singing begins, their voices should be well prepared. 
Have Pontius Pilate dictate a full and complete account of the trial and execution of a Galilean rabble-rouser, stick the scrolls marked with his official seal in a jar and bury it someplace where it’ll be found in the 20th century.
Another idea: talk Pilate out of crucifying him in the first place.
IIRC, Pilate tried to talk the rabble from crucifying Jesus, challenged the wisdom of Jesus’s sentence, knew Jesus had been framed, hell, even declared him innocent of any wrongdoing, eventually telling the crowd the death of Jesus was on their heads, not his, whereupon they accepted responsibility.
So it’s more “tell the Rabbi’s not to frame Jesus, or at least, don’t crucify the poor man!”
Well, I like today. Life is Good, all things considered. Screw up the past too much, even in what we think is a “better way” and today things may be fucked.
So, I’d go back, find the first tobacco plant and kill it. No smoking today.
Hmm, how about Solar power tech? Does anyone know enough about it here to say what we could bring back when to make solar a decade or more advanced? Maybe less Global warming?
I’d like to visit Philadelphia, PA for a few months beginning in May of 1787, buy James Madison a few tots of rum, and talk over Article Four; particularly the bits governing admission of states to the Union. I’d try to persuade him that there needs to be a process by which a state may leave (or even be involuntary expelled from) the Union.
If I can’t persuade him to put such procedures into Article Four, I’ll work on persuading him to make it explicit that admission is a one-way process, and is to be considered effective in perpetuity.
Missed the edit window: If either of my initiatives bears fruit, it will effectively prevent the Civil War. I note that, according to the terms of the OP, my project is supposed to make things worse, not better.
Does this disqualify me?
My daughter just asked me what I’m doing, and when I explained the assignment, she suggested that I set up a series of buoys along the sea lanes that served as the Middle Passage. The buoys would have signs declaring construction zones (yes, construction zones in the middle of the Atlantic Ocean), and directing ships to detours that would cause them to make landfall back in Africa, preferably in the harbor where they began.
And Columbus was too dumb to learn from his mistakes! According to history as I learnt it, after his first voyage he made several more, but continued to believe to his dying day that he had found India, or Asia at least. I’m sure the West Indies that found would not have fit any known descriptions of Asia or India. What? No spices?
If allowed, I would like to take 2 trips:
1- I will need a large extension cage, and haul as many stallions and mares (many of them pregnant by other stallions) as I can get, and drop them off in the North American plains around 500 AD. Depending on the size of your cage, I may also drop off wild pigs.
2- I will reappear around 800 and try like hell to introduce the idea of a written language to the native Americans, if they haven’t gotten it figured out for themselves by then.
Have long loved the idea of Columbo arriving to find a bustling early late middle ages society.
At the risk of scrubbing myself from existence, innoculate all the Native Americans (or teach them how to treat) against Smallpox, Typhus etc.
Sure, it may ultimately involve people dying, but I really want to see how it plays out.
Could I borrow the machine please to travel to around 50 A.D. (note - estimate, I might need a few trips to get the timing exactly right)? I need to find copies of early church records, in particular the “collected sayings of Jesus” whether or not there was actually someone of that name.
I’d arrange for multiple versions to be stored securely (Egypt/Sinai) would be a good candidate area) where they would be discovered in the 1880’s. Should be sufficient to create multiple moral/political crises across Europe and North Africa.
Of course, for maximum FUN just have them re-appear during the GW Bush Presidency, but not so much effect on history so far that way.