Homer's Barbershop Quartet - S5-E1
Continuity mistake: At the sale, when Bart and Lisa first find 'The Bee Sharps' album, the order of the records in the stack change in subsequent shots.
Continuity mistake: Just before Bart's flashback, his shirt is orange, and the chair he's sitting on is blue. But in this episode, his shirt is a paler shade of orange and the chairs in the classroom are red.
Continuity mistake: In the scene where Lisa runs into the attic as she dives behind the chest she rattles a bird cage, later when Ned faints you can see that the bird cage has disappeared.
Blood Feud - S2-E22
Audio problem: When Homer is kicking the postbox, Barney says something like "Fight the power" but his mouth never moves.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when the machine picks up the Simpsons' house, to take it to the 'Re-Neducation Centre,' the garage is on the wrong side of the house. It is on the correct side in the following shots of Homer returning. (00:11:20)
Continuity mistake: When Lisa knocks Bart's chop out his mouth she knocks it out front, however, the chop ends up going to the far right and into Homer's mouth.
Continuity mistake: When Krusty is sacked, his bottle of pop vanishes. (00:13:45)
Continuity mistake: At the end of the episode when Marge is first seen doing the entertainment, the shot shows (from left to right): Flanders, Skinner, Kirk Van Houten, Kent Brockman, Mayor Quimby, Grandpa, and behind them, Lionel Hutz, Lenny, Homer and Dr Hibbert. In a following shot from behind Marge the guests have changed places. Reverend Lovejoy is on the end, then Flanders, then Skinner, then Mr Burns, then Grandpa. There is a seat next to Grandpa which is blocked by Marge's head. Also Lionel Hutz has moved far back. Where did Burns appear from and where did Kirk, Mayor Quimby, and Kent Brockman all go?
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)
Kamp Krusty - S4-E1
Factual error: In the last scene, with the picture of the bus leaving Tijuana, it says "Leaving Tijuana" above the gate leading into the city.
Revealing mistake: When Smithers makes Mr. Burns his Wine Spritzer, Burns makes Homer Employee of the Month. While Smithers is pouring the stuff in the bottle, his left hand turns black for three frames. (00:10:30)
The Call of the Simpsons - S1-E7
Continuity mistake: When the cameraman is filming Homer in the mud, he screams quite a few times. Yet on the news report showing the footage, we only hear Homer yelling and not the screams. (00:16:00)
Itchy and Scratchy: The Movie - S4-E6
Audio problem: On the Itchy and Scratchy Movie ad, Itchy rips Scratchy's brain apart. He is laughing as well but his mouth doesn't move.
Continuity mistake: In the cafeteria at the power plant, in the wide shot the clock on the wall is on 9.00, but closer up it's showing 10.35.
Sideshow Bob's Last Gleaming - S7-E9
Continuity mistake: When Maggie (sitting on Marge) appears on "Tyrano-Vision," Homer waves his hand in front of her. However, we can see that he isn't leaning over too far, and in the next shot it is clear that both Bart and Lisa are sitting between Homer and Marge, so there is no way he could have reached over to her in the first place.
Much Apu About Nothing - S7-E23
Continuity mistake: When they are locating 'Springfield' on the map the coffee jug on the table is about 1/4 full.In the last shot of Apu the coffee has risen to about 3/4 full.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob leave Quimby's office, he had loads of things on his desk. When he pulls the picnic basket up, the desk is empty.
The Springfield Files - S8-E10
Continuity mistake: After the scene with the T-shirts, when the alien arives, Marge's "Homer is a dope" shirt disappears and she has her normal dress on.
Continuity mistake: At the end in the hospital, Maggie's bow is red for a second, then it changes to blue.
Thirty Minutes Over Tokyo - S10-E23
Continuity mistake: Marge loses one of her shoes in the "lava" , but when they fall down, Marge wears two shoes again.
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