Continuity mistake: At the end in the hospital, Maggie's bow is red for a second, then it changes to blue.
Continuity mistake: All through out the episode, Bart draws his pictures with only one pencil, but they all end up in color when he's done.
Continuity mistake: When Homer falls into the pool with green paint, most (but not all) of him is covered with paint. In the next close up shot, he's completely covered in paint.
Little Girl in the Big Ten - S13-E20
Continuity mistake: After Lisa's dream she lines up and the girl on the bars is the same girl the teacher told to go out.
Continuity mistake: When Homer gets out of the electric chair, the sponge has disappeared from on top of his head.
Continuity mistake: At the end of the episode when Bart, Lisa and Maggie greet their parents Bart says that they were in the Green Room (a room where the cast of a show can relax when not performing) and comments that '[he] ate so much shrimp!' This conflicts with the episode 'Please Homer, Don't Hammer 'Em', where it is revealed that Bart is allergic to shrimp.
Papa's Got a Brand New Badge - S13-E22
Continuity mistake: When Homer goes to the cupboard, there are no wires to the right of it. However, when Homer plugs in the singing Santa, there are lots of wires trailing to the right. (00:02:40)
Papa's Got a Brand New Badge - S13-E22
Continuity mistake: When the family is sitting on the couch and trying to catch a breeze from the fan, Lisa's shoes disappear between shots.
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