The Old Man and the C Student - S10-E20
Audio problem: At the end of the episode, Grampa's mouth doesn't move when he sings.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: During the song, Reverend Lovejoy at first has a blue sweater over his usual pink shirt, then he has a blue shirt, then he has his pink shirt without a sweater.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: When Dr. Hibbert says "Go ahead, girlfriend" at The Town hall, he is wearing a blue sweater, in the very next shot of everyone talking, he is wearing a pink sweater.
Wild Barts Can't Be Broken - S10-E11
Revealing mistake: Lenny's lower torso disappears for two frames when he, Carl, Homer and Barney are singing "We Are The Champions/We Will Rock You."
Audio problem: In the U2 scene during the end credits, when The Edge says "oh, here we go" his mouth is not in sync with his voice.
The Trouble With Trillions - S9-E20
Continuity mistake: The To Do Pile doesn't appear until Marge mentions it.
Continuity mistake: When the "Angel" tells everyone to prepare for the end, Carl is seen with yellow skin.
Continuity mistake: While everyone in Springfield is waiting for the apocalypse, Dr. Hibbert's wife Bernice is seen with yellow skin while she's holding on to him.
Continuity mistake: When Dr. Gould says the DNA test was inconclusive, Apu is seen in the background with yellow skin.
The City of New York vs. Homer Simpson - S9-E1
Revealing mistake: Homer drives his car through the man at the picnic.
Continuity mistake: After Milhouse explains to Bart how the warehouse collapsed, he appears to be bald for some reason.
Continuity mistake: During a shot of everyone at church, Carl is seen with a red sweater, after Homer says "Dammnit!", Carl's sweater turns blue.
The Old Man and the Lisa - S8-E21
Revealing mistake: At the hospital, while Lisa is explaining how much 10% of $120 million is to Homer, Dr. Hibbert's hand is yellow.
Homer vs. the 18th Amendment - S8-E18
Continuity mistake: Carl and Lenny are seen at both Moe's and at the St. Patrick's Day parade, which are happening simultaneously.
Brother From Another Series - S8-E16
Continuity mistake: Reverend Lovejoy is standing behind Sideshow Bob during his speech, but in one shot, he is standing with the protesters, then back behind Bob.
Brother From Another Series - S8-E16
Continuity mistake: While Sideshow Bob is walking out of prison and towards the protesters, Carl's hair is red.
Audio problem: Marge, Bart and Lisa are still heard "oohing" at the plumbing supplies store even after they close their mouths.
Continuity mistake: After Marge bites the candle down to a smaller size, the candle turns back to its original size for a frame.
Continuity mistake: During Bart's stand-up comedy routine, Dr. Nick is seen wearing his usual white lab coat, but in the very next shot of the audience laughing, he is not wearing a coat.
Revealing mistake: While Larry and Homer are talking about Mr. Burns, Larry's drink flickers light pink twice.
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