Tree House of Horror V - S6-E6
Continuity mistake: In "The Shinning", Homer looks into the mirror and you can see the carpet at the bottom of the steps is coloured pink. But when Homer falls down the steps in the next shot, the carpet is now green.
Tree House of Horror V - S6-E6
Continuity mistake: In "The Shinning", Marge goes to see the typewriter and you can see that viewed from behind the paper in the typewriter is crooked, but when the camera angle changes in the next shot, the paper is now straight.
Tree House of Horror V - S6-E6
Continuity mistake: In "The Shinning", Smithers is helping Mr Burns to put crates of beer into the car and you can see there is nothing on the lid on the car boot, but in the next shot a wheel appears from nowhere.
Continuity mistake: The cake that Marge bakes for Homer is initially white, but pink icing instantly appears on top between shots.
Continuity mistake: When Ralph comes to see Lisa, she is wearing her turquoise slippers. However, after he leaves and she drops the book on the floor, her slippers have gone.
Factual error: When Selma throws Moleman out of her car, the passenger door is hinged at the rear instead of The Front as it should be on a relatively-modern hatchback, and the window crank is visible on the outside of the door.
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.
Continuity mistake: When Homer is eating the sausage, a square on his shirt disappears in a shot from his feet and then is back in the next shot.
Other mistake: When Lisa says Bart's got a girlfriend, Bart says "no, I don't, that's the problem", his neck becomes longer and starts to wobble, a problem with the animation.
Strong Arms of the Ma - S14-E9
Audio problem: When Marge sprays the pepper spray at Ralph, the line she says after does not match her mouth.
Strong Arms of the Ma - S14-E9
Audio problem: When Homer says he'll eat twice as much, Bart says excellent, but that doesn't match his mouth.
Bart Gets an Elephant - S5-E17
Continuity mistake: Bart's elephant crushes the dog house, then it is shown standing, and then it is crushed again.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Lisa goes to save Clara, she's wearing the same dress she took to the dance, but after Clara walks safely back to land, Lisa is wearing another outfit entirely, then changes back to her previous outfit in the very next shot, then back to her unknown outfit seconds later.
A Totally Fun Thing Bart Will Never Do Again - S23-E19
Audio problem: While Bart is in the communication center, the second time Bart says "Squirt!", his lips don't move.
Politically Inept, with Homer Simpson - S23-E10
Revealing mistake: Right before Homer is patted down at the airport, his facial hair briefly flickers yellow.
Politically Inept, with Homer Simpson - S23-E10
Revealing mistake: While Homer catches his underwear with his tongue after the Simpsons' clothes burst out of the suitcases, Homer's tongue briefly passes through his underwear.
The Man in the Blue Flannel Pants - S23-E7
Audio problem: When the woman on the DVD Bart is watching says "Are you sure you're Martin Scorsese?" her mouth is completely out-of-sync with her voice.
The Man in the Blue Flannel Pants - S23-E7
Audio problem: In the rafting scene, while Marge says "And maybe when we get home, we can ride down something else?" part of her dialogue does not match her mouth movements.
The Man in the Blue Flannel Pants - S23-E7
Continuity mistake: While Krusty is talking to his merchandising executives, after Krusty says "Get to the point, unless you want a face full of clown chunks!" part of his collar turns green.
Audio problem: When Homer, Bart and Lisa enter E4, when Homer says "Wow", his mouth doesn't move.
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