Kill the Alligator and Run - S11-E19
Continuity mistake: When The Simpsons are being chased by the police, the cop is seen yelling at Homer. When the shot changes to Homer, the cop pulls out a gun from thin air and shoots.
Kill the Alligator and Run - S11-E19
Continuity mistake: The 2 guitarists in Kid Rock's band swap hair color when Kid Rock first arrives on stage.
Missionary: Impossible - S11-E15
Continuity mistake: When Q'Toktok says "I told you we should have asked them", his hair is black instead of grey.
Continuity mistake: During the revival meeting, Ruth Powers has a bandana on in some shots, and doesn't have it in other shots.
Continuity mistake: Homer was wearing a knit cap when the bucket fell on his head, but didn't have it when the bucket was removed. And since he was wearing a knit cap when the bucket fell on his head, his hair shouldn't have been ripped off when the bucket was removed.
Continuity mistake: In the dinner scene at the end, Maggie is not wearing a bow, but when everyone tells Moe "Merry Christmas", she has her bow on.
Tree House of Horror X - S11-E4
Continuity mistake: In "I Know What You Diddly-Iddly Did", Marge's necklace keeps changing from red to white when the Simpsons are at church, and when they go back home.
Continuity mistake: Just before Lisa's Presidential "refund adjustment" speech she pushes Bart's tape player off the desk and we can hear it smash off screen. Later in the episode when Lisa agrees to legalise it, he starts playing the same player.
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