Homer's Barbershop Quartet - S5-E1
Audio problem: When the Bee Sharps are singing 'Goodbye my Coney Island Baby' next to the Statue of liberty, you can hear Chief Wiggum's voice singing with the other members of the group, but he got chucked out of the group earlier on in the episode.
Audio problem: When Homer is talking to the family about their complaints about the nerds, he says something that ends in "where we can all live in harmony". When he says this the audio does not match his mouth movements.
Homer's Barbershop Quartet - S5-E1
Audio problem: When Homer is playing on the piano, he says the word "fault". When he says this you can hear a key being pressed but Homer doesn't touch any keys.
Homer's Barbershop Quartet - S5-E1
Audio problem: When grandpa is listening to the radio, he says something like 'oh.', but his lips are not moving.
Homer's Barbershop Quartet - S5-E1
Audio problem: After Jasper has sung on the stage to Homer, Apu and Skinner, they simultaneously say "Next". But if you listen carefully you can't hear Homer's voice.
Homer's Barbershop Quartet - S5-E1
Audio problem: In the scene where the Be Sharps first sing "Coney Island Babe" (I don't know what the song's really called) at Moe's, Skinner sings the rhythm. But when they sing the last few lines, you can still hear Skinner's part, but his mouth is moving like the rest of the group.
Audio problem: When Homer's vigilante group are putting out a leaf fire, Homer says "No burning leaves without a permit" his mouth is not moving.
Audio problem: After everyone congratulates Ned, he goes to Homer and his mouth moves but nothing is said, and the first line afterwards is not in sync with his mouth movements.
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