Continuity mistake: When the family are on the conveyer belt in the Knowledgeium, Homer turns round and grabs the handrail (after the Troy Maclure announcement) and his fingers are just touching the rail. In the next shot his hands are clasped to the rail.
Continuity mistake: When Homer's head gets caught in the middle of the draw bridge, a yellow stripe can be seen down the center of the bridge (where Homer has become stuck). However, in the closeup of Homer being hit by the cars, the stripe has disappeared.
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.
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.
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.
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: 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.
Revealing mistake: In the scene where Marge is cutting Grampa's hair, his left cheek in the mirror's reflection turns blue.
Continuity mistake: When we see the wide shot of all the houses going along the road, you can see that Moe's door is facing away from the Simpson's house. But in the next shot, Homer jumps in through Moe's door, it's like the tavern did a 180 degree turn.
Continuity mistake: When the family are walking through the car park after the visit to the Knowledgeium they walk by a purple car and there is a quick visual of a blue car in the bottom left hand corner of the screen.They immediately stop and they are now next to a pink and brown car.
Continuity mistake: At the garbage man debate, when Homer says 'Then you should have been early.', we see a shot of Lenny laughing. To the right of him, there is an old woman. In the next shot of Chief Wiggum, the same old woman is sitting to the right of him. In the later shot of Wiggum, Miss Hoover is sitting to the right of him and the old woman has disappeared.
Tree House of Horror VIII - S9-E4
Continuity mistake: Mutant Moe had one red mark on his face wile talking to Homer in the church, but when everyone attacks him, he has two.
Audio problem: At the Penitentiary gates when Ralph says 'Daddy's key went in there,' his lips don't move.
Lisa's Sax - S9-E3
Continuity mistake: In the episode 'Lisa's Sax' (season 9, ep. 3), King Toot's music store is across the street from Moe's Tavern. However, in numerous later episodes, there are stills of Moe's Tavern that show King Toot's music store next door, not across the street as in the aforementioned episode.
Continuity mistake: When Ralph and Bart are playing cards, Ralph has four cards in his hand. In a following shot he has five then back to four cards again.
Continuity mistake: At one point Marge says "no guns at the dinner table" and Homer says "you said the breakfast table", then Marge replies "it's the same table". In most episodes they eat dinner at a different table.
Continuity mistake: When Ray Patterson's / Homer's office is shown, the text on the door is different according to the different shots. When the shot is on the door, the writing on the window (Name and Sanitation Commissioner) is close together, but when the shot is from inside the office with the door open, the writing is apart.
Continuity mistake: When "The Leader's" car drives by, trailing a cloud of dust, the dust doesn't appear on the people's robes until the cloud clears away.
Bart Carny - S9-E12
Continuity mistake: When Principal Skinner is playing the ring toss game, in the end he only has one ring left in his hand. Then, after his mother asks "Why do you always fail?", he throws two more rings trying to win the combat knife.
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