Treehouse of Horror XIII - S14-E1
Continuity mistake: The people standing to the left of the rock, as the Comic Book Guy (as a faun) walks onto it, changes. In the first shot the police officers and Raplh stand there, in the second shot it's a panda. (00:19:25)
Treehouse of Horror XIII - S14-E1
Continuity mistake: When Homer starts to strangle his clone, the clone throws the boxes it was carrying, to the floor. In a following shot the boxes have vanished. (00:04:20)
Sleeping with the Enemy - S16-E3
Continuity mistake: When Lisa is making the game right at the beginning, we see her put a line at the bottom of her one, yet when the shot changes, it is gone. (00:00:25)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Chief Wiggum is running for the hot air balloon, you can see in the distance no one is in it, yet when he arrives Professor Frink is in it. (00:13:50)
The President Wore Pearls - S15-E3
Continuity mistake: When Lisa goes into Principle Skinner's office to resign, there is a mug and some papers on the desk. When she wants to use the microphone, the desk is clear.
Tree House of Horror XII - S13-E1
Continuity mistake: In the end title sequence, the frogman thing vomits and leaves a stain on the parking lot. When Pierce Brosnan drives away in his car, there is no stain. (00:21:05)
Continuity mistake: In the Meat video Jimmy's steak is first seen to be a little thin. In the closeup it's very thick, then thin again in the next shot.
Continuity mistake: When Maggie's dummy is spinning after the goat has taken her, the ground is clear. In the next close up shot there are tufts of grass and clumps of dirt there.
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: When we see the garden and Bart throwing Hymns into the fire the large tree is fully green. After the shot of Bart,the camera goes up and we see branches with no leaves on them though.
Tree House of Horror X - S11-E4
Continuity mistake: When Marge hits Ned Flanders, she pulls over, in the middle of the road. But When they go to see who they've hit, and when Homer picks Ned up and 'talks' to him, the car has disappeared from the road.
Tree House of Horror V - S6-E6
Continuity mistake: When the Simpsons shed their skin at the end, the skin falls to the floor. In the next shot it's gone.
Tree House of Horror V - S6-E6
Continuity mistake: In the third story, the five remaining students are all in one classroom - Bart, Lisa, Milhouse, Wendell, and Ralph. Ralph disappears when the other four try to escape.
Continuity mistake: At The Town hall meeting Mayor Quimby's microphone is first seen to be plain grey. In the following shot it has dark lines on it.
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart and Lisa are watching TV, Bart says something like 'I've got my ticket' and pats a ticket that is inside his shirt pocket (which there is none). But later in that same scene when they are still watching TV, both the pocket and the ticket have gone. (00:12:20 - 00:14:15)
Continuity mistake: The old men beside Grandpa when Homer plows the retirement home switch places, depending on whether it's a long or a close shot. (00:10:00)
Continuity mistake: As Homer is giving his speech to the dressed up monkeys, all of the monkeys are dressed in blue suits and you can also see there is one monkey next to the stairs on the stage. In the next shot of Homer leaving the stage there is now six monkeys, with only one wearing a suit and it is grey. (00:19:45)
On A Clear Day I Can't See My Sister - S16-E11
Continuity mistake: In Sprawl*Mart, the handle on the shopping cart disappears between the time Grandpa pulls the cart loose, and when you see him riding inside the cart.
It's a Mad, Mad, Mad, Mad Marge - S11-E21
Audio problem: When Becky is walking towards Otto in the wedding, there is a band playing music. You can hear singing but the singer's mouth isn't even moving.
Burns' Heir - S5-E18
Continuity mistake: A criss-cross pattern appears on the fireplace during the closeup on Smithers after Mr. Burns told him that he doesn't have a heir.
The Boy Who Knew Too Much - S5-E20
Continuity mistake: The American flag at the judge's right transforms to a plain white flag during the trial. (00:12:50 - 00:13:25)
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