Audio problem: When Matt Groening is putting boxes of comic books into the Comics Bongo Group truck, he says "I'm so rich" but his mouth isn't moving. (00:04:40)
Continuity mistake: When the wall is fully built, the people who put the wall up are several feet away from the rest of the people there. In the next shot, everyone is standing together. (00:19:20)
Audio problem: When Homer is placing objects on the dining room table to start his website, he is whistling but his mouth isn't moving.
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Audio problem: In "Clown Without Pity" when Homer is singing in the bath, his mouth doesn't match what he is singing. (00:05:20)
Other mistake: After Lisa has made Bart leave the baseball team, Lisa and the rest of the baseball team are having pepperoni pizza at Luigi's. Lisa is also eating the pepperoni pizza. However, Lisa is a vegetarian, so why would she eat pizza with meat on it?
I Love Lisa - S4-E15
Continuity mistake: When Homer and Bart are watching a clip of Sideshow Mel on wowee sauce and Bart then says "I'd give anything to go to that show", he has nothing in his hand. The shot cuts to Homer and he then says "I'd sell my first born son" and then the shot cuts back to Bart. When the shot cuts back to Bart, a Buzz cola can has appeared in his hand out of nowhere. (00:08:20)
In the Name of the Grandfather - S20-E14
Continuity mistake: When Grandpa smashes the hot tub, the pieces from the hot tub disappear moments later. (00:05:25)
Mypods and Boomsticks - S20-E7
Revealing mistake: When Bashir leaves the Simpson house, he doesn't have any eyebrows. (00:12:40)
Mypods and Boomsticks - S20-E7
Continuity mistake: When Homer runs into the old Springfield Mall at the demolition, if you look closely you can see Hans Moleman there. However, when the Duff truck crashes and Homer swims to save the beer, Hans Moleman is now in the truck. (00:18:30 - 00:19:05)
Continuity mistake: When the police arrive at the gate, Chief Wiggum is in one car and Lou and Eddie are in another car. But in the next shot, Chief Wiggum and Eddie are in the same car. (00:20:00)
Continuity mistake: When the fence between Springfield and Ogdenville is put up, Marge can be seen in a crowd behind all the people putting the fence up. In the next shot, Marge is next to the crowd of people who put the fence up. (00:19:20)
Other mistake: In the credits, Kristen Schaal is misspelled Kristen Schall. (00:20:40)
Continuity mistake: When the robber shoots Apu, he is shot around his leg. In the next shot, the wound is in his chest.
Other mistake: When Bart is looking at space through his telescope, Earth can be seen through the telescope despite him being on Earth.
Continuity mistake: When the Shelbyville kids drop the basket of lemons when Bart and friends start throwing lemons at them, the position of the basket changes when the Shelbyville kids run off. Note the colour of the Springfield grass and the Shelbyville grass.
Who Shot Mr. Burns? (1) - S6-E25
Other mistake: In the very first scene, when Principal Skinner is opening the door to the school, there is no name on the school. (00:00:25)
Continuity mistake: When Marge says good night to Bart he has pyjamas with sleeves on. Then when he puts on Lisa's nightgown (which doesn't have sleeves) to make Marge think he is Lisa, Bart's pyjama sleeves can't be seen under Lisa's nightgown. (00:12:25)
Continuity mistake: During the 20 years ago flashback, when Maude goes to spray water on Homer's pants, she is sitting on a tree in the background. When Homer and Marge talk, she doesn't spray water on his pants, but in the next shot she is gone. (00:17:35)
The Burns and the Bees - S20-E8
Factual error: When the bees fly to Mr. Burns' stadium, they are shown as seeing the stadium with 11 eyes. Bees only have 5 eyes. (00:18:15)
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