Continuity mistake: At the dinner table, we see an overhead shot of the table and there is a glass of milk next to Homers hand. As the shot changes, this glass is now gone from that location and moved to nearer Bart. (00:02:50)
Continuity mistake: When Marge and Homer are arguing over his boyhood dream, the time on clock jumps forward between shots. (00:13:20)
Continuity mistake: When Santa's Little Helper is eating from his bowl after his operation, the amount of food in his bowl increases drastically. (00:12:50)
Continuity mistake: When Bart is in the car and asks when the dog is going to get his operation, his hand is not on Lisa's seat. When the shot changes, to show the whole car, it is. (00:07:50)
Continuity mistake: When Homer is covered in gold and goes into Burns' office, Burns has 2 folders on his desk. One yellow and one white. However, the white folder becomes yellow in one shot. (00:04:50)
Continuity mistake: Homer asks Bart and Lisa what they will do with their money, Bart has a can of Buzz cola in his hand and when Lisa speaks the can simply vanishes from Barts hand. (00:04:20)
Continuity mistake: When Bart is pacing waiting for Sant's Little Helper, the time on the clock changes drastically when the nurse opens the door. (00:11:40)
Continuity mistake: When Homer suggests the family becomes a group of acrobats, a clipboard suddenly appears on the table in front of Marge. (00:11:30)
Continuity mistake: When Marge is listing all the cut backs, the calculator on the table keeps appearing and disappearing between shots. (00:10:30)
Continuity mistake: The colour of the sign Moe switches on at the start changes from yellow to red. (00:01:50)
Tree House of Horror VIII - S9-E4
Continuity mistake: Homer is dancing naked in the church and has his pants on the pew. There is then a wide shot and his pants are gone.
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: After the Germans have bought the plant, Homer takes a bite of his doughnut. The bite changes size between shots when Lenny and Karl ask him why he can't be fired. (00:09:10)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When the two Germans are looking at Homer in Moe's, the one's hand is on his paperwork. Camera cuts and it's half off the paperwork now. (00:05:20)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Homer pours his bottle of beer into his glass creating foam that is raised above the lip of the glass. Camera cuts and the foam has gone. (00:05:20)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Moe opens the special Duff and foam appears down the bottle that disappears instantly. (00:05:10)
Continuity mistake: When Moe gets up on stage with Aerosmith you can see the big "Flaming Moe's" sign behind them. However in the close up the sign isn't visible. (00:13:30)
Continuity mistake: When Martin tells Bart about the answers being worthless, Bart is stood by the grass or the kerb depending on the shot. (00:04:00)
Continuity mistake: When Bart gets off the bus there is a fire hydrant behind him. When we see the bus drive off the hydrant has gone. (00:07:10)
Continuity mistake: When Bart gets on the bus the day of the test, Milhouse is sitting at The Front of the bus. When we see Sherri and Terri looking at Bart, Milhouse has gone. (00:06:30)
Continuity mistake: When we see the big ape on the TV, the people running keep changing colour from black to white. (00:05:00)
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