Revealing mistake: When the announcer says that the Falcons win, he says "Who would've thunk it" Homer says "My daughter, that's who". When he is saying this, Lisa's arm disappears twice. (00:10:05)
Revealing mistake: When Homer leaves the bar after the Superbowl, as he goes through the door, the background is missing. It's just a brown background. (00:20:00)
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