Continuity mistake: When Homer leans back the lamp next to him changes from a red freestanding one to a blue table-top one. (00:02:40)
Continuity mistake: The position of the dots on Homer's pool change position. In the close up they're not near the water line but in the long shot they are. (00:03:10)
Continuity mistake: You may have to look carefully for this mistake. When Marge picks up the 'Das Butt' video, you can see the cover. In the next shot, you can see Marge holding it so you can't see the cover. But when she hands it over to Ruth, she twists the video round and you can see that nothing is visible. You may have to see it a couple of times. (00:04:50)
Continuity mistake: The position of the video in the basket changes between the first two consecutive shots. (00:04:50)
Audio problem: When Laura insults Kerney and Dolph, Dolph speaks but it's Jimbo's voice we hear even though Jimbo isn't there. (00:05:50)
Continuity mistake: When Marge and Homer are arguing about Don Quixote, Marge's pillow disappears from under her head. (00:09:50)
Continuity mistake: When Homer is sitting in the Frying Dutchman with the crowd gathered round looking at him, the Captain invites people in. Some start walking in, but in the next shot where they are all gathered round again, it is the same group of people again. (00:17:00)
Other mistake: When Moe is running to the Simpsons' house there is a shot of him running past the moon. When running back to the bar, the same shot is used but is simply flipped. Note the house and rocks. (00:18:20)
Continuity mistake: In the episode "New Kid on the Block," Bart says his home address is 1094 Evergreen Terrace. In "Homer the Vigilante," his home address is 723 Evergreen Terrace; and for the rest of the series, it has been 742 Evergreen Terrace. (00:18:30)
Plot hole: When Bart prank-calls Moe and tells him his name is Jimbo Jones, Bart says that he lives at 1094 Evergreen Terrace instead of 742 Evergreen Terrace, where Jimbo and Bart are. If Moe had taken those directions, he wouldn't have arrived at the house, instead he would have gone somewhere different. (00:18:30)
Continuity mistake: When Moe confronts Jimbo, Jimbo has his back in a corner with just a cabinet behind him. When the shot changes he is next to the green chair. (00:19:00)
Audio problem: When Laura tells Bart she has a boyfriend, Bart imagines her ripping out his heart. If you listen and look carefully, you will see the sound of Laura's hand ripping out Bart's heart comes before Laura even touches him.
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