Recently, Matsby wrote about how much he disliked Quantum Leap, largely because of times when they wouldn't stick to their own rules. Love it or hate it, at least the show got people thinking and talking about the possibilities of time travel.
For example, in one episode Sam Beckett teaches the song "Peggy Sue" to Buddy Holly. But when you think about it, the only way that Sam Beckett could know the song is if Buddy Holly came up with it on his own. If the only reason Buddy Holly knew the song "Peggy Sue" was because Sam Beckett traveled back in time to teach it to him, and Sam Beckett couldn't know the song unless Buddy Holly created it on his own, then the song should never exist.
Maybe Buddy Holly came up with the song on his own, but later in life. That means that Sam Beckett's time travel just meant that Buddy Holly came up with the song earlier.
It reminds me of Star Trek IV, where the Enterprise has traveled back to the 1980s to bring some whales to the future. To get them out of a jam, Chief Engineer Montgomery Scott (aka Scotty) gives the formula for "Transparent Aluminum" to some scientist. The formula for transparent aluminum wasn't discovered until far into the future.
When Dr. McCoy (aka Bones) chastized Scotty for giving away the formula and potentially messing with the timelines, Scotty said "How do you know he didn't invent the thing?" Dr. McCoy seems satisfied with Scotty's answer and they carry on with presumably no tangible effect on the timeline.
What Scotty doesn't realise is that if that guy actually was the guy to invent transparent aluminum, then we have the same sort of paradox: that guy couldn't have invented it unless Scotty gave it to him, but of course Scotty wouldn't know the formula itself unless that scientist had invented it on his own. Transparent Aluminum couldn't exist.
The only way to avoid the paradox is if that scientist did invent it on his own, but later on, so Scotty just helped him invent it earlier. Or if some other scientist had invented it in the original timeline, but in this new timeline he doesn't bother because it was already invented. In this case, it was only "invented" because Scotty gave it to the first scientist, making yet another paradox.
If this isn't a paradox, then you could essentially create anything - anything at all! Go back to the past and teach an inventor how to create something, and then it'll be created, giving you the knowledge to give it to the inventor. In fact, you could even use this to invent the time machine itself.
I guess in the end what I'm saying is that if you ever travel to the past, don't teach anyone anything.