Continuity mistake: At the institute, Dave puts his hand on his son twice, and they also swap positions between shots. (00:10:00)
Continuity mistake: At the Institute, the clipboard Dave is holding repeatedly switches arms between shots. It also disappears entirely. (00:09:35 - 00:10:35)
Continuity mistake: When the family are walking through the car park after the visit to the Knowledgeium they walk by a purple car and there is a quick visual of a blue car in the bottom left hand corner of the screen.They immediately stop and they are now next to a pink and brown car.
Audio problem: When Lisa visits Homer at the plant, they are playing astronauts with the radiation suits. When they spin around and around, Homer is laughing but his mouth stays the same.
Continuity mistake: When Homer is in space, when he is about to free the ants, the crisps that he opened earlier have disappeared from the background. This type of mistake happens again when both the crisps and the ants disappear and reappear between shots.
Continuity mistake: Near the end of the episode, when Skinner shouts at Ralph to shut up, the sky outside the bus changes from nighttime to daytime between shots. (00:14:15)
Continuity mistake: After Sideshow Bob finishes reading his book and puts it on the table, the pages of the book change from yellow to red between shots.
Factual error: When the creator of Danger Dog draws a picture of Skinner on a notepad and puts it on the projector, it is perfectly visible. It shouldn't have been, seeing as the pad was so thick.
Continuity mistake: When Bart is talking to Jessica after she stole the collection plate money, she is far away from Bart. But when Bart says "but you're not very nice", she is right next to him.
Continuity mistake: As Bart is forced to show Marge the item (picture frame) he is hiding, he pulls it out of his jacket and he hands it to Marge. As he pulls it out you can see there is nothing in the frame or on the border of the picture frame. After Marge's reaction to the photo we see a close up of the frame and there is now a picture in the frame and some colorful decorations around the frame. Whilst the frame could have been the backside when he pulled it out he never turned it over when handing it to her, and Marge never turned it around when looking at it.
Tree House of Horror VI - S7-E6
Continuity mistake: During the 'Nightmare on Evergreen Terrace' segment, when Bart is running from Willie, he plans to sink Willie in the sandbox. In the first view of the sandbox it is isolated on a field, yet when Willie is sinking in the sand there is a jungle-gym beside the sandbox. (00:11:35)
Continuity mistake: At the garbage man debate, when Homer says 'Then you should have been early.', we see a shot of Lenny laughing. To the right of him, there is an old woman. In the next shot of Chief Wiggum, the same old woman is sitting to the right of him. In the later shot of Wiggum, Miss Hoover is sitting to the right of him and the old woman has disappeared.
Moaning Lisa - S1-E6
Continuity mistake: When Bart and Homer first play the video boxing, the window behind them shows that it's broad daylight outside. When Homer blames his loss on Lisa's Sax, it cuts to Lisa's room and it's night all of a sudden.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer wipes the tobacco on his forehead in his new class, the tobacco just disappears on his hand/sleeve.
Special Edna (a.k.a. Love and Marking) - S14-E7
Factual error: During the video screening at the Teacher of the Year committee, the panel is watching the teacher who acts like Robin Williams. In the video the main judge says "Next" and pushes a button on the video control. It goes to the video that Bart Simpson sent in. How was this possible? The video control would only fast forward the video and two separate entries would not be sent in on the same tape. The committee wouldn't have spliced the footage together onto the same tape as the tapes were piled up on the desk. At the start of the scene one of the judges mentions to put in the next tape.
Continuity mistake: Bart opens the house's front door, then the shot zooms out to show us that all of Springfield is at the Simpson house. In the next shot with Mayor Quimby the door is suddenly closed. (00:15:30)
Continuity mistake: During Tom Savini's presentation, the comic book seller eats a kind of cookie. Fake blood then start to flows from his mouth and he takes his t-shirt to wipes it. There are no stains on it after that.
Tree House of Horror VIII - S9-E4
Continuity mistake: Mutant Moe had one red mark on his face wile talking to Homer in the church, but when everyone attacks him, he has two.
My Mother the Carjacker - S15-E2
Other mistake: In the scene where the prisoners are singing along with Mona, two inmates have the same Identity number.
Treehouse of Horror XIII - S14-E1
Audio problem: When Homer is playing the piano, and Marge is playing the cello, Frink grabs Homer and pulls him into the room. However the playing of the piano continues, even after Homer is pulled away. (00:13:50)
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