Continuity mistake: Before the time trials start, the audience on the sidelines keep disappearing and reappearing. (00:12:30 - 00:13:40)
Continuity mistake: When Otto announces about Milhouse's party, 1, Martin is sitting two seats ahead of Bart and Milhouse, even though he was just talking to them, and 2, Sherri and Terri are nowhere to be seen. (00:01:35 - 00:02:35)
Continuity mistake: When Bart realizes he forgot his permission slip, the camera shows us that the paper is half-under his pillow. However, when he got out of his bed at the very beginning, the paper wasn't under his pillow. (00:01:00 - 00:03:05)
Continuity mistake: When Lisa is clapping erasers because she sassed Miss Hoover a second time, the room's clock is visible near the top of the ceiling. However, the clock wasn't there several shots earlier. (00:17:00)
Continuity mistake: At the end of the episode when Mr. Burns rotates his desk to turn off the power, the ink block and fountain pen to his left change position.
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.
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