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.
Much Apu About Nothing - S7-E23
Continuity mistake: During the party for Apu, Dr. Nick is first seen not wearing a coat, then he has his usual white coat, then he has a brown coat, and then the white coat again.
22 Short Films About Springfield - S7-E21
Revealing mistake: A black line briefly appears on Apu's forehead while he's tossing the tofu dog around.
Audio problem: When the car drives into the cornfield, Martin is heard screaming, even though he is still asleep.
Continuity mistake: In the overhead shot of Patty smoking, she is sitting on a greenish-gold car, the car then turns blue in the next shot.
Continuity mistake: When Homer gets up to make Mr. Burns' breakfast, Marge's nightgown is yellow, making her look naked, but in the next shot, her gown is purple.
Continuity mistake: At the funeral, while everyone is clapping for Bob Newhart, Mayor Quimby is seen with brown skin.
Scenes From a Class Struggle in Springfield - S7-E14
Audio problem: Homer's mouth is completely out of sync when he says "our savings?"
Team Homer - S7-E12
Revealing mistake: When the children are running down the hallway, the animation keeps repeating. Duplicates of the same children are running several times.
Three Men and a Comic Book - S2-E21
Audio problem: When Homer offers to take the family to Krusty Burger, Lisa is heard cheering, even though her mouth is closed.
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