Continuity mistake: On the trip back from the gardens, Homer rear ends the car in front of him on the bridge which sends Maggie flying out of the car. In a long shot of the bridge whilst Maggie is in the air you can see the car has changed to an orange color instead of the usual light purple color. The two cars in front of them also change during shot. The one in front of the simpsons changes from a normal red mid sized car to a blue van, whilst the car in front of that one changes from being a green car to a blue one during the aerial shot of Maggie.
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: Right at the beginning of this episode, Homer is wearing a watch on his left hand, and he is still wearing it in one shot when he's in the car, but when he reclines his chair it is gone. (00:00:30)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The remote control for the robot in Bart's bedroom appears from nowhere. (00:08:30)
Burns' Heir - S5-E18
Continuity mistake: When Mr. Burns is sitting in front of the fireplace, he has his normal blue outfit when seen from behind, and a purple night gown when seen from The Front. (00:02:50)
Like Father, Like Klown - S3-E6
Continuity mistake: In Krusty's story after he has his makeup washed off by a rabbi, just after his father speaks to him his makeup suddenly reappears. (00:09:40)
New Kids on the Blecch - S12-E14
Continuity mistake: When L.T. Smash switches the lever to Commission from De-Commission, after that, when the shot changes, it says Ship and Museum. (00:18:10)
Continuity mistake: When Homer bangs on the screen in the testing booth, the little sign on the top left of the glass that was there earlier is no longer there.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: Marge puts down 2 glasses of juice and a baby bottle on the table when she is telling the kids about the marriage problems. but when she walks away in the next shot, the glasses and bottle are gone.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: In Dr. Marvin Monroe's office, in the first shot, we can see a garbage can beside his desk. It disappears for the rest of the scene. The desk also moves forward. (00:13:35)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: As the family looks out the window to see the limo, the light switch on the wall has vanished. (00:03:40)
Continuity mistake: When the newspapers fall on Skinner, the rake in the corner has turned into a shovel. (00:19:10)
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Early on in this episode, Mr Burns says something like "this positivly has to be there overnight", the shot goes closer on every word or so. You can see that the background behind Mr Burns is that of the Plant. But when the shot zooms out, the background is now of one of the corridors.
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 Marge comes to pay for her shopping, she empties her left pocket on her coat, but when Sanjay finds it in her pocket, it's in her left pocket. We know it wasn't in her pocket anyway because when Sanjay finds it, it is bigger than the size of her pocket.
Lisa's Pony - S3-E8
Continuity mistake: At one point in the episode, Homer is on the phone with someone in his work station. I forget who it was, but anyway, when you first see him, the wire is coming from the left side of him and when he turns to his right, the wire is coming from the right side of him.
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.
There's Something About Marrying - S16-E10
Continuity mistake: Reverend Lovejoy is unable to cite which book in the Bible condemns homosexuality, but in "Homer the Heretic," he is able to recite, from memory, a completely random Bible verse.
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.
Continuity mistake: In the opening scene of the episode, envelopes are pushed through a mail-slot on The Front door. However, when Laddie arrives and Bart goes outside to meet him, The Front door's mail slot has disappeared.
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