Audio problem: After Homer and Marge steal Gil's balloon, they fly towards clothes, Marge says "Clothes! We're saved!", but her mouth dosen't move.
Revealing mistake: When Marge stands up at one point in the airplane restaurant, her legs and part of her dress have disappeared.
Continuity mistake: While Lisa is standing in front of the table with her friends in the cafeteria, we see that the trays appear during the first shot, then after the camera zooms in on Lisa's table, the trays disappear. Then during the third shot, Lisa calls Alex over to her table. Look at the table again: the trays have reappeared. (00:06:00)
Continuity mistake: After Lisa wakes from her daydream, there's a boy behind her with blonde hair and a light purple shirt. After Ms. Hoover says "Then come back and finish the test", the boy's hair turns blue, and after it zooms in on Lisa's face, there's a boy with brown hair and a blue shirt behind her.
Continuity mistake: While in the cafeteria, Principal Skinner asks Milhouse to lower his eyebrows. Behind him, there is a bulletin board that changes from brown to purple.
The Wizard of Evergreen Terrace - S10-E2
Continuity mistake: When Lenny is telling his story, his 5 o'clock moustache keeps changing from brown to grey.
The Wizard of Evergreen Terrace - S10-E2
Continuity mistake: During the very last scene Homer is sitting on the sofa next to Bart watching the news. But in the last shot he's sitting in a separate chair next to the sofa.
Continuity mistake: The bible that Reverend Lovejoy returns at the library is bigger in the first shot.
Continuity mistake: When Bart says "Everybody, come quick!", the fridge door goes from open to closed.
Continuity mistake: In this episode and maybe in other one, the door to the basement is at the entrance of the house, but that's a closet in other episode.
Revealing mistake: When Marge says, "Slow and steady wins the race", her face and body are two different colors.
Factual error: When Bart is at Nelson's house and Nelson is firing the BB gun, bullets should come out of his gun when he pumps it. None ever come out, and several times he is shown firing without pumping.
Tree House of Horror IX - S10-E4
Audio problem: At the end when Bart says 'Don't forget Ken Star' his mouth doesn't move.
Tree House of Horror IX - S10-E4
Continuity mistake: In "Starship Poopers," Kang always wears a glass thing on his head, but whenever Homer beats him up, it's gone.
When You Dish Upon a Star - S10-E5
Continuity mistake: In the shot just before Alec gets hit by a tree branch, his watch is missing but in the next shot, his watch gets snagged on something.
When You Dish Upon a Star - S10-E5
Revealing mistake: At court, as Homer is walking towards Alec Baldwin, Kim Basinger and Ron Howard, Bart is in the background sitting with the rest of the Simpsons, but his head is missing from his body. His head then reappears back on his body after about 2 seconds.
When You Dish Upon a Star - S10-E5
Revealing mistake: When Homer and the family are having hamburgers at the dinner table, at one point you can see the oven. The pointer on one of the dials is misaligned.
Audio problem: In the beginning, we are at the power plant. We find out that Burns has packed his own lunch, and one thing he packed is a bullion cube. His mouth doesn't move right when he says "Bullion cube".
Continuity mistake: When Homer is shot at the hippie farm, he ends up with a flower in his head, stem first. But he put the flower in the gun barrel stem first, as well. From a shot at that close a range and that velocity, there's no way the flower could have turned around in mid-air.
Continuity mistake: When Lisa is in Principal Skinner's office, there isn't a scoreboard control panel on the desk, yet when there is an overhead shot of his desk, one suddenly appears.
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