Continuity mistake: When Mr. Burns notices that Homer is wearing a pink shirt to work, when he pauses and zooms in the video, Homer is looking almost directly at the camera. In the next shot, though, he is looking more to his left. The people surrounding him also change. (00:03:05)
Continuity mistake: Bart opens the house's front door, then the shot zooms out to show us that all of Springfield is at the Simpson house. In the next shot with Mayor Quimby the door is suddenly closed. (00:15:30)
Continuity mistake: After "Michael" comes out of the Simpsons' car, there's a shot of the crowd's shocked reaction. Oddly, Groundskeeper Willie seems to have grey hair and brown skin.
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