Continuity mistake: Lenny's mug refills itself when he tells Homer, "You want to help me?"
New Kids on the Blecch - S12-E14
Audio problem: When the VJ on the TV says "That was the latest ad from Stridex pads. Medicated", her mouth is terribly out of sync with her voice.
Revealing mistake: When Lisa wraps herself in Marge's arms right before she falls asleep, the inside of her mouth turns yellow.
Continuity mistake: After Amy Tan shames Lisa, there is a shot of Lisa wearing a red necklace, her necklace becomes her usual white one, seconds later.
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.
Audio problem: Superintendent Chalmers' mouth doesn't move when he says "Idiot."
Audio problem: When Homer says "According to my driver's license, I weigh 140 pounds" his mouth is not in sync with his voice.
Continuity mistake: After Lisa wakes from her daydream, there's a boy behind her with blonde hair and a light purple shirt. After Ms. Hoover says "Then come back and finish the test", the boy's hair turns blue, and after it zooms in on Lisa's face, there's a boy with brown hair and a blue shirt behind her.
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.
Brother's Little Helper - S11-E2
Audio problem: Homer's mouth is out of sync when he's naming celebrities who use drugs.
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.
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