Homer's Barbershop Quartet - S5-E1
Continuity mistake: When you see a shot of the church from outside in the scene where the bee sharps sing there, look closely at the sign. It says 'Also: The Bee Sharps', only they don't name themselves that until later on in that episode.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: In the flashback where Marge is making a model of Homer, the models head falls off and Santa's Little Helper picks it up, but the Simpsons did not own the dog back then.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: At the sale, when Bart and Lisa first find 'The Bee Sharps' album, the order of the records in the stack change in subsequent shots.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: At the end of the episode, while the B-sharps are singing on top of Moe's Cavern, the guy climbing the building asks the people to look at him. As he moves his hands, his gloves change color from red to white and back to red.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: When Homer is talking to George Harrison, he sees that he has a brownie. Then he rushes over to a pile of brownies and starts scoffing them down. The pile of brownies doesn't get smaller.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: In the deleted scene where the Be Sharps unveil 'Donut Records', Barney's hair flashes red a couple of times in the close-up of the band.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: Homer and Marge's bedroom has photos of Bart and Lisa when they were 10 and 8 years old. However, the story takes place when Bart and Lisa were only 3 and 1.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: When Bart and Lisa find the record Melvin and the Squirrels, they hand it to the Comic Book Guy to play. While the record is in his hand you can still see it displayed on the rack.
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