Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Homer crashes through the security barrier then skids to a halt on concrete. But, a shot later, the car is on a field which wasn't there before.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Principal Skinner picks up the hamster and throws it away. But his hands are clean as a whistle even though all the hamster was covered with oil.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: In this episode, Mr Burns and Smithers are on the balcony of Burns' office. Mr Burns says "It will be like taking candy from a baby. Hey, that sounds like a laugh. Let's try it right now." We see Smithers, whose expression doesn't change as the two go back into Burn's office. In 'Who Shot Mr Burns Part 2', Smithers remembers this event, except now he looks quite shocked when Burns mentions about taking the candy.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: During The Town meeting scene, the position of Latin jazz great Tito Puente hops all over the room - he is frequently appearing in the background, but from various angles.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Smithers and Mr Burns are eating the chocolate and see the photo, you can see that Marge's necklace changes from red to white and then back to red.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Burns is pretending to be a student in Skinner's office, the door changes from open to closed and from dark blue/green to grey.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Early on in this episode, Mr Burns says something like "this positivly has to be there overnight", the shot goes closer on every word or so. You can see that the background behind Mr Burns is that of the Plant. But when the shot zooms out, the background is now of one of the corridors.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Mr. Burns is sitting on Principal Skinner's desk, he takes his cap off and places in on the desk next to him. But in the next shot when Skinner is saying his monopoly is terrible, the cap is gone.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Mr. Burns falls onto the sundial, everybody starts gathering around. Marge is there, with Maggie. She left Maggie in the car and seeing as she went off to look for Homer, Bart, Lisa and Grandpa and that she was one of the first on the scene when Mr. Burns collaspses, it would be difficult to run back and get Maggie from the car.
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.
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