Revealing mistake: When Bart is swinging on the clothes line into the night, it is obvious that the brightness has been turned down because the sky is the same colour as in the previous shot. If it were night time, then the sky would be a dark purple colour. (00:04:20)
Homer's Triple Bypass - S4-E11
Continuity mistake: In this episode, Homer closes the curtain on Ned when he is praying. And the curtain is blue. However, a few scenes afterwards, when Homer is talking to Krusty, the curtain is green/beige. (00:14:10)
Continuity mistake: When Homer and Marge come home from the dinner, Marge is wearing a fancy dress. But when Bart falls out of the house right after Homer walks in, she has her typical green dress on. (00:06:15)
Continuity mistake: When Selma is on video at the end of the episode, the iguanas's eyes change from yellow to white during the scene, but not between shots.
Audio problem: At the end of the episode the statue of Jimmy Carter with Marge's hairdo is unveiled, and the assembled throng applaud her reaction. They are all chattering away, but no sound is coming out of their mouths - we only hear the sound of clapping.
Continuity mistake: After Krusty is done doing the special promotion commercial, he is given a telegram informing him of the Soviet boycott. However, this is a flashback, and at this point in time Krusty is illiterate (as will later be established in season 1) so he shouldn't be able to read the telegram. (00:12:30)
Other mistake: When Homer is crossing the rickety bridge in the snow plow there is no snow on the planks even though he is in a blizzard and the storm couldn't have just started because the path he just came from was covered in snow. (00:18:55)
Last Exit to Springfield - S4-E17
Continuity mistake: When Mr Burns is telling Homer to resign, he has glasses on in the first shot in the scene. However his glasses are on his desk the next shot onwards.
Character mistake: Lisa states that Pierre and Marie Curie both died of radiation poisoning. This is incorrect, as only Marie died of radiation poisoning while her husband Pierre was killed by a horse and cart. (00:08:30)
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)
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: Lionel Hutz runs out of Burns' office leaving both doors open. When Marge says about going, they are closed. (00:20:20)
Continuity mistake: When Homer is talking about Marge getting a job at the dinner table he has a spoon in his hand. Once Marge has finished scowling he doesn't, and there isn't one on the plate either. (00:08:05)
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)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Homer is about to punish Bart, his ticket suddenly appears in a shirt pocket. (00:15:10)
Continuity mistake: The position of the video in the basket changes between the first two consecutive shots. (00:04:50)
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)
Revealing mistake: When Grandpa is reading from the book trying to find out what is wrong with Maggie, the pages are blank. (00:09:30)
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