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.
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.
Cape Feare - S5-E2
Continuity mistake: At the beginning of the episode when we see MacBain on TV he goes through a curtain, the curtain stays open for a second even though he isn't touching it.
Cape Feare - S5-E2
Continuity mistake: When Bob has finished singing the score of the H.M.S. Pinafore, an English flag comes down. But when he draws his sword to kill Bart, the flag is gone. Where could it have gone?
Cape Feare - S5-E2
Continuity mistake: When Bob is working out on the weights, he has a tattoo of something on his knuckles, but when he is watching the exercise video, the tattoo dissappears.
Continuity mistake: Just after Homer has used the proton accelerator, Dean talks to him. In this scene he is writing something on a piece of paper, but he writes on the same line every time. He finishes writing on that line, then starts on it again.
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.
Continuity mistake: The colour of the alien poster in the nerds' room changes from pink to blue.
Revealing mistake: When we see people digging Bobo out of the ice, they put him in a bag. If you look carefully you can see another Bobo put in another bag just before the shot changes.
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In "Terror at 5 1/2 Feet", when Milhouse decides that he is going to sit next to Uter, Uter all of sudden moves to the other side of the seat between shots.
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: At the end just before the Simpsons say "Happy Halloween everybody" they are about to bite Lisa (and make her a vampire). Maggie has no dummy (or in America, pacifier) in her mouth, but it suddenly appears when she closes her mouth.
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Other mistake: When Bart says the picture of the school bus is actually called The Ghoul Bus, Lisa points out the name tag says The School Bus. If you closely at the name tag, you can see nothing is written on it.
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: When Otto hits Hans Moleman's car, it has a number plate on it, which disappears when he crashes.
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: Just before Homer is sucked into Hell, he is wearing pyjamas. When he's in Hell, he's wearing his usual day clothes.
Other mistake: When Homer and Chief Wiggum fall into the waste, in the second shot, the cliff edge looks very weird. It seems to be transparent with Ruth's car floating in mid-air, and there is a big curved wall that doesn't have ground at the top.
Continuity mistake: When we first see the power sander, there is only a white patch on the side. In the next shot when we return to viewing it, "Property of Ned Flanders" has appeared.
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