Continuity mistake: As Homer is giving his speech to the dressed up monkeys, all of the monkeys are dressed in blue suits and you can also see there is one monkey next to the stairs on the stage. In the next shot of Homer leaving the stage there is now six monkeys, with only one wearing a suit and it is grey. (00:19:45)
Continuity mistake: When the Stonecutters are singing "We do", the position of several characters, particularly Number 51 and Chief Wiggum, change randomly as the camera angles change. Number 51 starts at the end of the table on the right side, with Chief Wiggum two seats to the left of him. In later shots, Number 51, then Wiggum are both switched to the same position, midway up the left side. Then, when the song ends, Wiggum has disappeared, and Number 51 remains in this new position.
Continuity mistake: During the "We Do" song, there is a character at the top of the screen who keeps changing colour. I think it might be Dr Hibbert, but his skin colour keeps flickering to yellow.
Continuity mistake: When Homer starts walking away with the stone of shame, you can see he has no birth mark on him. yet in the next shot all off the stonecutters see the birthmark.
Continuity mistake: When Mr. Burns pushes the child on the swings, he somehow manages to defy the laws of physics. When he pushes the child forward for the last time, he swings forward, then back, hitting Mr. Burns in the head. He then swings forward again, hitting Mr. Burns from behind. Mr Burns starts saying "You've won this round..." and the child then hits Mr. Burns from behind again. In order for this to happen, he would have to go completely around between the second and third hits and you clearly see he doesn't.
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