Continuity mistake: When Flanders walks up to the door, there is nothing next to the door, but in the next shot after Homer has thrown garbage onto him, there is an egg box next to the door.
Continuity mistake: When the garbage man is asking Homer if he learned anything from love day, his cigarette is in his hand, but in the next shot when Homer says, "That was yesterday moron", the cigarette is now in his mouth.
Continuity mistake: When we see the wide shot of all the houses going along the road, you can see that Moe's door is facing away from the Simpson's house. But in the next shot, Homer jumps in through Moe's door, it's like the tavern did a 180 degree turn.
Continuity mistake: At the garbage man debate, when Homer says 'Then you should have been early.', we see a shot of Lenny laughing. To the right of him, there is an old woman. In the next shot of Chief Wiggum, the same old woman is sitting to the right of him. In the later shot of Wiggum, Miss Hoover is sitting to the right of him and the old woman has disappeared.
Continuity mistake: When Ray Patterson's / Homer's office is shown, the text on the door is different according to the different shots. When the shot is on the door, the writing on the window (Name and Sanitation Commissioner) is close together, but when the shot is from inside the office with the door open, the writing is apart.
Continuity mistake: When Homer is running down the street with his garbage, it spills out all over the road. But in the next shot when the garbage men are confronting him, all the garbage is gone.
Audio problem: In the U2 scene during the end credits, when The Edge says "oh, here we go" his mouth is not in sync with his voice.
Continuity mistake: At one point when Homer is giving his speech in front of the Jebediah Springfield statue, Carl's skin is yellow. In all other shots he is back to his normal color.
Continuity mistake: At one point, while everyone is clapping for Homer during the debate in The Town hall, Apu is seen with yellow skin, and Chief Wiggum is seen with black hair among the townspeople. In all other shots, they're back to their normal skin and hair color.
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