I'm surprised no one has made any Quantum Leap jokes yet.
So yes, after answering a lot of the great mysteries of the ages (the various proclaimed patsies of the era of assassinations in the 60s; the 'alien crash' at Roswell; Jesus; chicken or the egg), I'd have to do a few things on my list.
Buy several boxes of Beta magic cards -- 10, preferably. I wouldn't sell them for profit. I'd just love to go to Gen Con and offer a "Beta Magic Draft" with an entry fee of only $9 (which is about what the cards would cost). I can only imagine how much joy that would bring to some people.
At least once I'd have to knock on the door of my ex-girlfriend while she was . . . involved with someone else. No hard feelings, but I figure she deserves a bit of a hard time for it.
Yeah, I'd go see Star Wars. In England, since that's where my father was stationed at the time. And then I'd invite my dad, my mom, and my older brother (who would be about four months old at the time) out to dinner afterward to talk about how cool it was.
I wouldn't do this, but I think this would be a great way to show that a time traveling villain is a massive bastard. Have him go to Mt. Vesuvius the day before the eruption and offer people vast sums of money to buy their boats. Then just burn all the boats and leave.
I'd bring the current staff and all the computers of Industrial Light & Magic back in time to 1984 and tell George Lucas to go for it! Just, y'know, to see if he'd always been insane, or if it truly was the result of the monster that lives in his neck.
Get a couple of very strong guys to shanghai Kurt Cobain and then fake his death. Ditto Elvis and Jimi Hendrix and Jim Morrison and Jim Belushi and Janis Joplin. Get them into a group therapy session. Or a jam session.
One week before GenCon 2000, go up to Monte Cook and show him the 3.5 edition of the PHB.