Audio problem: When Laura tells Bart she has a boyfriend, Bart imagines her ripping out his heart. If you listen and look carefully, you will see the sound of Laura's hand ripping out Bart's heart comes before Laura even touches him.
Audio problem: When Milhouse is saying he's getting swimmer's ear, his mouth is out of sync whilst saying it.
Audio problem: When the bus is flying off the bridge and Otto says "Which way should I turn?" look closely at him when we can see his face during the line. We can see his mouth is out of sync when he's saying it.
Audio problem: When Homer says God is his favourite fictional character, his mouth is saying something different to what we hear.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Audio problem: When Marge says "Save our families" at the beginning of her petition, her mouth doesn't move. (00:14:40)
Audio problem: When Homer says "I need change for a dollar. I also need a dollar", his mouth doesn't match what he's saying. (00:07:25)
Audio problem: When Matt Groening is putting boxes of comic books into the Comics Bongo Group truck, he says "I'm so rich" but his mouth isn't moving. (00:04:40)
Audio problem: When Homer is placing objects on the dining room table to start his website, he is whistling but his mouth isn't moving.
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Audio problem: In "Clown Without Pity" when Homer is singing in the bath, his mouth doesn't match what he is singing. (00:05:20)
Audio problem: After being hit with the nuclear waste, Ranier Wolfcastle says "My eyes! The goggles do nothing" without moving his mouth.
Audio problem: When Bart is going through his keys, he says "Your house", and his mouth doesn't match what he is saying.
Audio problem: When Marge says "We've gotta get to the hospital, Homer" her mouth doesn't move.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Homer and Bart go to destroy the beaver dam, Homer says "Oh, boy" without moving his mouth.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Bart attempts to free Homer from the beavers, he says "I'll save you", but his mouth doesn't match what he's saying.
Dude, Where's My Ranch? - S14-E18
Audio problem: At the recording studio, when Homer sings the Frankenstein and Dr. No line, his mouth doesn't match what he is saying.
Audio problem: When Homer says "Burn the truth" after burning his pants, his mouth doesn't match what he is saying.
Brother Can You Spare Two Dimes? - S3-E24
Audio problem: When Lisa says "I stand corrected" at the award ceremony, her mouth doesn't match what she is saying. (00:07:25)
Thirty Minutes Over Tokyo - S10-E23
Audio problem: In America Town, when Bart says "These prices suck. 10,000 Yen for coleslaw?", his mouth doesn't match what he is saying.
Audio problem: When everyone runs towards the cooler on the next morning, they all cheer but their mouths don't move. (00:13:20)
Audio problem: When Bart takes Milhouse's inhaler to go after the cooler, Milhouse says "Hey, I need that to live". His mouth doesn't match with what he is saying. (00:12:15)
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