Revealing mistake: When the bartender points to the Fudd neon sign behind him, his hand goes through the sign. (00:05:40)
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)
Revealing mistake: When Homer is putting up all the lost dog posters on the building that gets blown up, the stapler isn't on the poster. (00:17:30)
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)
Burns Verkaufen der Kraftwerk - S3-E11
Other mistake: When Burns is writing on the back of the big cheque, the writing suddenly appears in one block. (00:10:05)
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)
Audio problem: When Moe says "I'll talk to you tomorrow" to Homer, his mouth doesn't move. (00:15:15)
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)
Audio problem: When Krusty arrives at the bar, Bernard says "Hey Krusty" but his mouth doesn't move. (00:11:00)
Other mistake: When watching TV at the start Homer's beer can just says D instead off Duff. (00:02:15)
Like Father, Like Klown - S3-E6
Other mistake: When Krusty leaves the Simpsons, The Front door is just an empty space missing all the details. (00:11:20)
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