Continuity mistake: At the start, the remote on the sofa next to Homer simply vanishes and returns when Marge walks in. (00:00:40)
Radio Bart - S3-E13
Continuity mistake: The position of the hole Homer is digging changes position in relation to the well. (00:19:40)
Continuity mistake: When Marge is opening the letter and pulls the money out, the shot changes and the money is no longer in her hand. (00:16:20)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Homer is talking to the two German's at Moe's he puts his glass on the bar. When the shot changes it's up in the air and no longer on the bar. (00:05:20)
Continuity mistake: Lisa asks Homer to go to Dr Hibbert's office, when she does, Homer's hand on the window changes places between shots. Note the vertical bars. (00:15:50)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Burns says he needs to get his plant back. When he does the door behind him is open or closed depending on the shot. (00:19:00)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Homer can't sleep, if you look out the window you can see a house in the distance. When the shot changes this house should be visible but it isn't. (00:11:20)
Continuity mistake: When McBane's partner asks him to do just one thing for him, the picture keeps appearing and disappearing from his hands. (00:05:30)
Lisa's Pony - S3-E8
Continuity mistake: When Ralph is sat on the fence watching Lisa, his position changes between shots. Note the fence post in relation to his body. (00:15:20)
Lisa's Pony - S3-E8
Continuity mistake: When trying to get a loan, Homer is tapping his fingers on the counter. When the shot changes, his hands are by his side. (00:10:00)
Continuity mistake: The angle of the door at the end changes from partially open to fully open instantly. (00:20:30)
Continuity mistake: When the one member of Aerosmith invites Moe up on stage his guitar simply vanishes. (00:13:40)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: At the start the amount of soap by Burns' head changes drastically and instantly. (00:01:30)
Continuity mistake: In the garage Homer rolls up one sleeve but in the next shot both are rolled up. (00:10:35)
Continuity mistake: When Lisa asks for a virgin Moe, Homer's Duff can is missing its colourings. (00:11:10)
Lisa's Pony - S3-E8
Continuity mistake: When applying for the loan, a bell appears on the counter in front of Homer. (00:10:00)
Revealing mistake: When the car arrives at the NFI, the car goes straight through the barrier. (00:09:20)
Continuity mistake: During the Planet of the Apes musical segment, just before Troy McClure sings "Can I play the piano anymore?", he and Dr. Zaius are standing far apart. In the next shot, they are close together.
Continuity mistake: After Phil eats the "horse" egg at Moe's he asks to be taken to the hospital, and when it cuts back to Homer at the power plant, the direction of the stripes on Homer's tie switch to the opposite direction, mid shot. The same thing occurs again later. First, when Homer is standing outside the office while Fred talks to Burns about the benefits package, and also when Homer can't stay for Marge's turkey breakfast. (00:07:05 - 00:12:20)
Continuity mistake: While Homer, Carl, and Lenny are at Moe's with their new bud Fred, in the interior shots the swinging front door to Moe's swings open on the left side, but in the exterior shot when they all leave Moe's, that door still swings open on the left side, opposite to the interior shots. (00:08:00)
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.
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