Continuity mistake: When Bart arrives at school in the bus, after Homer plowed the road for the bus, the sidewalk is covered in snow except for Martin's footprints. Then, when he gets out, the sidewalk has been shovelled, as there is no snow on it. Following this, Bart is pelted by snowballs, which sends him falling face-first into the sidewalk, which is once again covered in snow. (00:10:20)
Continuity mistake: When Homer hands over the key to Mayor Quimbey, the mayor points out the teeth marks on it. But in the next shot when Homer says he thought there was chocolate inside, the bite marks are gone. (00:16:30)
Continuity mistake: In the bit where they sit on the sofa at the start of each episode, there is one rather long one where it starts off with the Simpsons dancing in a line, then gradually evolves into a circus with elephants and men dancing around fire. Look closely in between Homer's right leg and the dancing woman on his right. There is a pile of books on the little shelf underneath the lamp and telephone, and just as the camera starts zooming out from the line of dancing, the orange book on the left noticeably changes to purple. (00:01:20)
Continuity mistake: When lying on the sofa at the start, Bart's raised leg switches between instant cuts. (00:02:30)
Continuity mistake: In one scene Bart is swinging on a washing line then we see Homer talk to Marge and he says "He'll soon get tired of it" then it goes back to Bart and he is facing the opposite direction and he is swinging on two washing lines. (00:04:22)
Continuity mistake: When we see Marge leave Bart with Patty and Selma, they are stood with a gap between them. Camera changes to focus on the sisters, and they are now next to each other. (00:06:30)
Continuity mistake: When the flashback of Ned and Todd Flanders singing in the Simpsons' doorway, Homer says he could use a TV tray. Then it goes back to the present time and Homer picks up a beer from the TV tray which is next to the couch. The TV tray was never there at any other point in the show. (00:10:40)
Continuity mistake: After Krusty is done doing the special promotion commercial, he is given a telegram informing him of the Soviet boycott. However, this is a flashback, and at this point in time Krusty is illiterate (as will later be established in season 1) so he shouldn't be able to read the telegram. (00:12:30)
Continuity mistake: Rodd's hair is black when him and Todd are in bed singing. It can't be because it's dark, because Todd's hair is unchanged. (00:15:10)
Homer's Triple Bypass - S4-E11
Continuity mistake: When Bart says about a train wreck near the start, the items on the table between his and Lisa's bowls changes between shots. (00:02:50)
Homer's Triple Bypass - S4-E11
Continuity mistake: When Homer is eating the bacon and what looks like scrambled eggs after claiming Marge's oatmeal had a bug on it, the close up of the bacon shows that it is pink/purple and the eggs are yellow but the in the following shot, when Bart says, "Dad, there's a bug on that." the bacon and the eggs switch colours. (00:03:40)
Homer's Triple Bypass - S4-E11
Continuity mistake: When Dr Nick visits Homer for the first time, he leaves the door open. But later before the reporters come to the door, the door is closed. (00:13:40)
Homer's Triple Bypass - S4-E11
Continuity mistake: In this episode, Homer closes the curtain on Ned when he is praying. And the curtain is blue. However, a few scenes afterwards, when Homer is talking to Krusty, the curtain is green/beige. (00:14:10)
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