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
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)
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)
Other mistake: When watching TV at the start Homer's beer can just says D instead off Duff. (00:02:15)
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)
Continuity mistake: When Homer puts Lisa's test on the fridge, a lot more papers appear on the fridge. (00:04:50)
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)
Like Father, Like Klown - S3-E6
Continuity mistake: At the end of Krusty's story the candles have burnt themselves out on the table. However in the next shot they are alight again. (00:10:05)
Like Father, Like Klown - S3-E6
Continuity mistake: Towards the end of the meal, Lisa has some meat left on her plate that disappears in some shots completely. (00:06:55)
Like Father, Like Klown - S3-E6
Continuity mistake: When talking about Jewish people, Homer puts mashed potatoes on his plate that sometime disappear and reappear. (00:06:30)
Like Father, Like Klown - S3-E6
Continuity mistake: Lisa says about Krusty being Jewish and Homer's wine glass swaps side on the table. (00:06:20)
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