Revealing mistake: In the scene where the family is in the car, driving home from The Town hall meeting, Homer says "the whole reason we have elected officials is so we don't have to think all the time!" When he says "don't" a second collar appears beneath the right collar of his shirt, and then disappears after he says "time." (00:11:20)
Revealing mistake: When a comet is about to hit Springfield, everyone is standing on a hill in the shadow of it. But the shadow is still there even after it breaks up.
Revealing mistake: When everyone is in Ned's shelter, the woman in the top left hand corner with brown hair and brown skin briefly has 2 pupils in each eye.
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer