Continuity mistake: When Homer leans back the lamp next to him changes from a red freestanding one to a blue table-top one. (00:02:40)
Continuity mistake: Lionel Hutz runs out of Burns' office leaving both doors open. When Marge says about going, they are closed. (00:20:20)
Revealing mistake: When Grandpa is reading from the book trying to find out what is wrong with Maggie, the pages are blank. (00:09:30)
Continuity mistake: When Homer is talking about Marge getting a job at the dinner table he has a spoon in his hand. Once Marge has finished scowling he doesn't, and there isn't one on the plate either. (00:08:05)
Continuity mistake: We see the items fall off the roof but a Christmas ornament is not among them. However one lands on the ground with everything else. (00:02:05)
Continuity mistake: When stuff is falling off the roof, in the long shot there is nothing on the roof but in the close up there is. (00:02:05)
Itchy and Scratchy: The Movie - S4-E6
Revealing mistake: When Lisa is trying to explain to Homer about Bart seeing the movie, one of the pearls on her necklace keeps disappearing and reappearing. (00:18:20)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Homer is about to punish Bart, his ticket suddenly appears in a shirt pocket. (00:15:10)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: What the goats are eating changes depending on the shots. (00:10:10)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: Homer asks Bart if he took the bins out. When Homer walks into the kitchen, the time on clock changes. (00:10:00)
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Continuity mistake: When Homer finds out the doll is trying to kill him, the popcorn moves from the sofa onto his lap. (00:04:40)
Homer Alone - S3-E15
Continuity mistake: When Marge has finished the list of things to do at Rancho Relaxo she has a list on the bed. When we next see Marge a few seconds later, the paper is gone. (00:17:50)
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)
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