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)
Audio problem: After being hit with the nuclear waste, Ranier Wolfcastle says "My eyes! The goggles do nothing" without moving his mouth.
Tree House of Horror XI - S12-E1
Continuity mistake: In the "Scary Tales can Come True" segment, Bart's plague rat bite disappears for the rest of the segment.
Continuity mistake: During Lisa's and Bart's segment, time seems to run really quickly. When Lisa leaves West Springfield Elementary it is 11:00 and when she gets to Moe's it is noon, then a few minutes later it is 2:50. When Bart and Milhouse find Fat Tony it is noon, then when Bart gets hit by the truck, it is almost 3:00.
Audio problem: When Bart is going through his keys, he says "Your house", and his mouth doesn't match what he is saying.
Audio problem: When Marge says "We've gotta get to the hospital, Homer" her mouth doesn't move.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Homer and Bart go to destroy the beaver dam, Homer says "Oh, boy" without moving his mouth.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Bart attempts to free Homer from the beavers, he says "I'll save you", but his mouth doesn't match what he's saying.
Dude, Where's My Ranch? - S14-E18
Audio problem: At the recording studio, when Homer sings the Frankenstein and Dr. No line, his mouth doesn't match what he is saying.
Continuity mistake: When Bart goes up to his treehouse to write the kidnap letter, he throws his Murder 4 Life jumper out the treehouse entrance. Later, when Lisa finds the jumper, it is now on a tree branch as if he threw it out of one of the treehouse windows.
Audio problem: When Homer says "Burn the truth" after burning his pants, his mouth doesn't match what he is saying.
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