Continuity mistake: When Homer goes to apologise to Lisa, he walks into her room and leaves the door open. As he steps inside however the door is now closed. (00:15:50)
Continuity mistake: When Lisa is lying on the floor, she has 3 pieces of paper/notepads with her. Once she starts to ring Moe though, there are only 2 pieces of paper on the floor. (00:12:05)
Continuity mistake: When Homer is yelling at the TV about being wrong 48% of the time, the colours of his beer can are reversed. (00:03:40)
Continuity mistake: At the start, the design on Homer's beer can change. Note the white stripe. (00:00:55)
Continuity mistake: When Homer is eating the snacks at the start, he drips some dip on the sofa that vanishes when Marge appears. (00:00:50)
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)
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