Continuity mistake: When everybody is chanting 'Film Festival', you can see that Mayor Quimby has his arm up. But in the next shot, which changes so that you can see Marge, he his holding up his other arm.
Continuity mistake: During the lamb vision at dinner Lisa is holding her knife and fork. In the very next shot they're on the table.
Continuity mistake: When Sadgasm is making their first appearance, Homer says, "We are Sadgasm," and there are a few students walking around, but when he says, "And this song is called 'Politically INcorrect'," there is a big crowd in front of them with no time to form one.
Miracle on Evergreen Terrace - S9-E10
Continuity mistake: When Bart pulls the melted tree out of the house, a shovel appears out of thin air so he can shovel snow onto it.
Lisa's Rival - S6-E2
Continuity mistake: When Nelson does his "Grapes of Wrath" demonstration, it splatters all over Skinner's jacket. When he walks over to the rest of the dioramas his jacket is clean again.
Homer Badman - S6-E9
Continuity mistake: When Homer mixes the Pop Rox with the soda he leaves the Pop Rox packaging over the can. After he throws the can and we see it in the air the Pop Rox packaging has disappeared.
Large Marge - S14-E4
Continuity mistake: After Homer paints "El Homo" on the wall, he paints over it so that none of the letters are visible. In the next shot a couple of the letters are visible, and are only struck out with one line.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: At the very start of the episode, Moe is wearing a watch. But in the next shot when all the guys come in, and all following shots, the watch is gone.
The Great Louse Detective - S14-E6
Continuity mistake: Frank Grimes' gravestone appears to look different from "Homer's Enemy" and "Alone Again, Natura Diddly."
Tree House of Horror X - S11-E4
Continuity mistake: When the flashback of running over Ned happens his jumper is ripped and sleeveless because he has just been a wolf. Earlier though when the Simpsons find him, his jumper is not ripped.
Continuity mistake: Throughout the whole of this episode, the clock on Mr. Burns' desk keeps appearing and disappearing.
Radio Bart - S3-E13
Continuity mistake: When Rod and Todd talks to 'God' on the radio, the antenna keeps changing position for the entire scene. (00:08:50 - 00:09:40)
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Thing and I' Dr. Hibbert is about to explain Bart's irregular birth. In the closeup before the story, Dr. Hibbert has a stethoscope around his neck. This wasn't there in previous shots. (00:03:50)
Large Marge - S14-E4
Continuity mistake: In some shots, the incorrectly-colored lobsters have their claws taped shut, and in others they don't. It's completely random.
Tree House of Horror VIII - S9-E4
Continuity mistake: When Homer pulls up to the stoplight, the number of cars in front of him changes. When he first stops, there are 3. When he gets out of the car, there is only 1.
Continuity mistake: When Milhouse is spying with his binoculars with an camouflage outfit on, the colours of some patches change in some other shots. E.g The bottom left corner (from behind) changes from dark green to light green.
Continuity mistake: In the scene when Homer is signing up for the naval reserve, the administrator gives him a pencil to fill out his form, but when the camera moves to The Front of Homer it changed to a pen.
Papa's Got a Brand New Badge - S13-E22
Continuity mistake: When Homer goes to the cupboard, there are no wires to the right of it. However, when Homer plugs in the singing Santa, there are lots of wires trailing to the right. (00:02:40)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Samantha is being introduced to the class, there is a boy in The Front row on the right side that is wearing a white shirt and has brown hair. A few shots later (an overhead shot of the classroom), the boy is completely different, with a blue shirt and white hair. (00:04:00)
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