Burns' Heir - S5-E18
Continuity mistake: When Mr. Burns is sitting in front of the fireplace, he has his normal blue outfit when seen from behind, and a purple night gown when seen from The Front. (00:02:50)
Secrets of a Successful Marriage - S5-E22
Continuity mistake: Marge puts down 2 glasses of juice and a baby bottle on the table when she is telling the kids about the marriage problems. but when she walks away in the next shot, the glasses and bottle are gone.
The Last Temptation of Homer - S5-E9
Continuity mistake: In this episode when Homer comes home from work, The Front door opens on the wrong side than it usually does.
Sweet Seymour Skinner's Baadasssss Song - S5-E19
Continuity mistake: When Marge, Bart and Lisa are watching the videos at the beginning of the episode, the clock changes from one time to a completely different time between shots.
Continuity mistake: When Homer drives his car to work it is lime green instead of the usual purplish color.
Homer's Barbershop Quartet - S5-E1
Other mistake: When Bart and Lisa are looking at records, there is a picture of Homer. He had hair at the time the record was made, and the hat he's wearing isn't big enough to cover it, but there's none visible as there should be.
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. (00:15:40)
Continuity mistake: In the opening shot of Apu serving his customers, you can see Martin wearing a purple shirt. However, later when all the customers are grumbling about the price, you can see Martin walk away wearing a white shirt.
Factual error: As Bart, Homer, Ned and Todd drift away from land in their boat, we see the clouds moving away. The clouds would not move that fast at the speed that the boat was going.
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.
Sweet Seymour Skinner's Baadasssss Song - S5-E19
Continuity mistake: In the air duct, the dog comes up behind Willie in a straight line and licks his feet, we saw what the duct looked like when Willie turned around. However, when the children start throwing stuff at the duct, from the outside there is a sharp bend right behind where Willie and the dog are that wasn't there in the internal shots.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer sees Marge and Moe near the end, the coffee table changes size between shots. It's large when Moe sits on the couch.It's smaller when there's a shot of Homer and long again when the high shot shows Homer walking out (when his rags are stuck on it)
Burns' Heir - S5-E18
Continuity mistake: When Homer says, "You idiot," to the programmer, the red ashtray changes position on the desk. (00:15:55)
Burns' Heir - S5-E18
Continuity mistake: Burns' top hat disappears from the bath at the start.
Continuity mistake: During the wedding, when seen from behind Reverend Lovejoy, there is no podium in front of him (although his hands are poised in mid-air as though one should be there). In the reverse shot, the podium has magically reappeared. (00:20:00)
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.
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: As Bart is on the phone trying to book his new act, you can see there is a split down his white shirt. When the shot changes and he tells Lisa to be quiet you can see that split has disappeared. (00:15:05)
Continuity mistake: When Bart is writing from the books in the kitchen, he is seen writing on the paper. In the next shot of him, the paper is clean.
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When Lisa and Marge go on the tour, when the film has finished the woman turns it off with a remote controller and puts it behind her back. In the next shot from behind her it isn't in her hands and there is no sign of a pocket or any indication she put it anywhere else.
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.
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