Among our primary criticisms of the show Quantum Leap are all the ontological paradoxes that are created, and never explained.
Indeed, while the time travel premise of he show is intriguing, as is the idea that he actually takes the place of someone in the past, the show essentially uses time travel as nothing more than its premise, and never really explores the field.
The ontological paradoxes alone are enough to drive you crazy. He teaches Buddy Holly the lyrics to Peggy Sue, gives Stephen King the plot to Christine, and - most seriously of all - he even gives his time travel theory itself to an earlier version of himself (albeit accidentally).
Some of us dislike the show because it would establish rules in one episode only to be broken in another, and some of us dislike it because the time traveller is trapped in time and never seems to make any kind of effort to return home, but we all dislike it because it never seems to make even the slightest effort to examine time travel in a plausible way.
Note: Occasionally we get together to review time travel movies, discussing their approaches and how they relate to today's theories. You can check out the one we did for Back to the Future, and we've recorded one for Star Trek that's coming soon. In the mean time we're taking suggestions for what to review next. Please either email us your requests, or post them as comments here - but please don't ask for Quantum Leap!