Monty Can't Buy Me Love - S10-E21
Continuity mistake: Ralph Wiggum is seen riding the train inside the mall, but is seen some seconds later amongst the crowd of people still waiting to enter the store.
Monty Can't Buy Me Love - S10-E21
Continuity mistake: Bart is next to Homer when Marge says "Where did you get that champagne?", but in the next shot, a clown is in the spot Bart was.
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: 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.
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