Homer Alone - S3-E15
Continuity mistake: When Barney is kneeling by The Front door step, a pool of water appears next to him instantly. (00:16:40)
Revealing mistake: When Homer leaves the bar after the Superbowl, as he goes through the door, the background is missing. It's just a brown background. (00:20:00)
Continuity mistake: At the bar when Homer is watching the superbowl, his hands keep changing position between the shots. (00:19:00)
Continuity mistake: Homer picks up Lisa who puts her Malibu Stacey down on the bed. When Homer puts her down, the doll and house have disappeared. (00:16:30)
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: Just as Barney asks Homer if he wants to go bowling next Sunday, Moe's boot disappears from the bar and the money appears in Homer's hands off the bar. (00:12:20)
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: When Homer gets off the phone to Moe, all the snacks he had have simply gone beyond a few remaining bits. (00:02:00)
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: 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)
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)
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: 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)
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