Treehouse of Horror XIV - S15-E1
Continuity mistake: The piles of sweets and candy that Bart and Lisa have at the start vanish in the wide shots when Homer arrives.
Continuity mistake: When Krusty enters the Jewish Walk of Fame building, there are no stars on the pavement outside it. When he leaves there are. (00:06:15)
Continuity mistake: When Homer writes an autograph for Ralph at the restaurant, Lisa is sitting opposite Marge, has yellow liquid in her glass and has red and brown food on her plate. In the next shot, Lisa is opposite Homer, has a blue drink and has white and green food. (00:14:25)
Continuity mistake: When Homer leaves the studio after being cancelled there is no sign next to the door. When Marge walks up to comfort him there is now a 'stage door' sign there. (00:18:35)
Continuity mistake: When the pile of newspapers fall on principal Skinner, two garbage cans appear out of nowhere beside the door. (00:19:10)
Thirty Minutes Over Tokyo - S10-E23
Continuity mistake: When Homer breaks into Flanders's house there's a shot of the refrigerator and nothing is on it. In a closer shot, there are tickets being held up by a magnet.
Tree House of Horror XII - S13-E1
Continuity mistake: In 'Hex and the City', Marge and Homer swap places at the wedding.
Tree House of Horror X - S11-E4
Audio problem: In "Desperately Xeeking Xena", Xena is put in a plastic pouch. Wouldn't her voice sound muffled?
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when Homer exits the basement, he discovers Bart and Lisa are giants, and he then screams and runs back to the "basement" - however the same door that leads to the basement seconds ago, now leads to a green -carpeted room, and the basement seems to have vanished. The door is also hinged on the wrong side. (00:12:50)
Itchy and Scratchy: The Movie - S4-E6
Audio problem: When Homer says 'My child is on the honor roll at Springfield Elementary', you can see that his mouth is not moving. (00:04:25)
Continuity mistake: When Homer is talking to Ned about having his own BBQ Ned is facing the fence but in the next shot he is facing alongside it with his head turned to Homer.
Tree House of Horror VIII - S9-E4
Other mistake: In 'Homega man', Homer goes into the bomb shelter and does not shut the door, and you can still see it open for a while after he is in there. Herman does not close it behind him - you can tell by his skeleton's position. But Homer opens the door to leave the shelter after he has eaten the food, and it must have been closed for him to have survived the atomic attack, because it vaporised Herman, who was only a few feet away.
Continuity mistake: When Homer and Bart are at the cabaret show, Mr. Burns and Smithers are there with two women. In almost all of the shots there is a woman sitting between Burns and Smithers, except in the close-up of them when Burns asks "How does he DO it?". Then Smithers is shown as sitting right next to Mr. Burns. (00:21:00)
Other mistake: After Ugolin (one of the French men looking after Bart) has taken Bart to the Chateau Maison, Cesar and Ugolin speak. (they aren't visible in this shot) Ugolin says "Escape is impossible", but the subtitles say that Cesar says it and vice versa for when Cesar actually speaks.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: At Sunday school, Milhouse's jumper changes from black to red between shots.
The Call of the Simpsons - S1-E7
Revealing mistake: The scientist who describes Homer as a brilliant beast seems to have some of his hair magically floating above his ear - it's not connected to his head, yet it moves alongside his head. (00:20:40)
Home Away From Homer - S16-E20
Continuity mistake: When Homer rings the doorbell of the Flanders' former house to visit the new neighbour, it moves downwards on the door frame. In the first shot it lines up with the gap between the lock and the doorknob, but in the next shot it is beside the doorknob, and in other shots in the episode the doorbell isn't even there. Also, the glass panels on both sidelights line up with the door differently between shots.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer tries to tell Marge how he did in the test, Selma and Patty are holding their cigarettes. In the next shot, the cigarettes are in their mouths.
The Secret War of Lisa Simpson - S8-E25
Continuity mistake: When Lisa climbs to the top of the Eliminator, there is a platform for her to stand on. Strangely in the next shot Lisa is standing on nothing so she appears to be standing in mid-air.
Continuity mistake: The photo Edna sends to Bart differs when he shows his parents. The angle is different from what it was previously, revealing part of a photo frame on the wall which wasn't there before, and the sheets/pillows on the bed are different, and her eyes are closed when they look at it, but when Bart looked at it, they were open. (00:09:05 - 00:18:25)
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