Continuity mistake: After Homer dodges the cannonball near the end of the episode, the blue platform that he stood on goes further away from the edge of the stage between shots, and when Homer hugs Marge the platform has disappeared and Peter Frampton's cooler has become closer to Homer.
Continuity mistake: When Homer is on stage in Springfield and preparing to get hit by the cannonball, the speaker-tower, behind and slightly to the left of him, completely disappears in the wide shot right before Homer jumps off stage.
Audio problem: Just after Homer has been knocked down by the cannon with the "No Litter" message on his stomach, you hear cheering but the crowd don't do anything.
Continuity mistake: After Homer is shot with the cannon for the first time, the cannonball disappears from behind him.
Continuity mistake: When Homer is taking the kids to school for the second time the view behind him doesn't look further away while driving.
Continuity mistake: In the scene where Homer is on stage in Springfield, he's wearing shorts. When he jumps off the stage after dodging the cannon ball, he's wearing pants.
Continuity mistake: In the scene where Homer dodges the cannon ball, he is wearing goggles and a helmet. But when Homer jumps down from the platform and hugs Marge, his helmet and goggles have disappeared.
Continuity mistake: The X-rays of Homer's intestine change sides between shots when he is at the vet.
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