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.
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)
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.
Pygmoelian - S11-E16
Continuity mistake: When Moe is going to get a plastic surgery, the surgeon draws some marks on his face. You see Moe from a side view, and the marks on his face aren't visible from that angle. However, the marks on his face suddenly appear and you can now see them from that angle.
Like Father, Like Klown - S3-E6
Continuity mistake: When Reverend Lovejoy gives Bart a t-shirt "Gabbin' about God", Bart puts it behind his back, where it disappears in the blink of an eye. Look closely (pause helps), but it definitely does disappear. (00:13:40)
Continuity mistake: When Homer falls down the gorge, the medics lift him up on a bungee and to the top of the cliff. Between shots the edge of the cliff changes from green grass to brown rock. (00:20:05)
Bart Carny - S9-E12
Continuity mistake: When Bart starts Hitlers' car moving, for a couple of shots the "Iron Cross" disappears from the side of it.
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