The Call of the Simpsons - S1-E7
Continuity mistake: When Homer is driving through the river, in one shot while Marge is talking, Homer's vest and shirt switch colors (from green shirt and grey vest to grey shirt and green vest). (00:07:15)
Continuity mistake: When Homer talks to Bart about ties, the two strands of hair on top of his head are missing. (00:09:20)
Continuity mistake: When Ms Melon is talking to Bart during the chemistry experiment, she is holding her clipboard with one hand on the back, but in the next shot she is holding the board with both hands on the side.
Continuity mistake: When Richard, Milhouse and Lewis are playing marbles in the school playground, behind Lewis there is only a tree, but in the next shot a table appears from nowhere.
Continuity mistake: When Homer goes to see Bart in his bedroom, the door goes from being open to closed between shots.
Continuity mistake: At lunch, two boys exchange Bart's sandwich for a grape. When they give him the grape, it lands in Bart's right hand but in the next shot he has it in his left hand, and when one boy gives Bart a cup, the grape is back in his right hand again, and in the shot after that, the two items have changed positions.
Continuity mistake: When Ms Melon is showing Bart his new classmates in the classroom at the Learning Center, you can see that Bart is standing in front of a wooden sculpture in one shot, but in the next shot he is standing in front of the bookcase.
Continuity mistake: When Homer and Bart arrive at The Enriched Learning Center, they go to the classroom and you can see there is a sign outside the room saying "Learning Center: Grade IV." But when we see the two a little later on, the writing has gone.
Continuity mistake: When Homer hands Principal Skinner the cheque, the back of the cheque is coloured yellow but changes to white a little later on. (00:07:20)
Continuity mistake: When Bart is in Principal Skinner's office, there is a voice box on the right hand side of the desk. But when Principal Skinner looks into the filing cabinet, the box has gone. (00:06:40)
Continuity mistake: When Bart picks up his chair after falling during the intelligent test, you can see there is only a pencil on his desk. In the next shot, his paper appears from nowhere. (00:06:00)
Continuity mistake: During the intelligence test, the table on Bart's paper changes between shots.
Continuity mistake: When Bart and the three other boys are standing by the wall after Bart sprayed a drawing of Principal Skinner, there are bushes by the end of the wall. But when we see Martin standing by the drawing, there are no bushes.
Continuity mistake: When Homer grabs hold of Bart's arm and demands to know what a "Kwyjibo" is, he is holding a brown skinned banana in his left hand. The banana remains in his hand when Bart is forced to explain what a "Kwyjibo" is, but when Homer begins to chase Bart, the banana has gone. (00:03:10)
Continuity mistake: When Homer picks up the yellow book from under the settee, you can see there is a white label on The Front cover. But when Lisa is reading the book, the label is now on the back cover, and when we see Lisa a few shots later, it is back on The Front again. (00:02:40)
Continuity mistake: When Marge is speaking to Homer during the Scrabble game at the beginning, you can see the tray in front of her is full of tiles. But when Homer takes away the book from under the settee Marge is sitting on, a piece has disappeared. (00:02:05)
Factual error: Bart uses Milhouse's glasses as binoculars, but as Milhouse is near-sighted this wouldn't work.
Continuity mistake: At the "Do What You Feel" Festival, Homer shows up in his house robe, bear feet styled slippers, unshaven, and unbrushed hair. When he takes the float to save Bart, he's in his regular clothing of blue pants, white shirt, shoes, and clean shaven.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer gives Ms Botz her money when she is in her car, she takes it but in the next shot the money is nowhere to be seen.
Some Enchanted Evening - S1-E13
Continuity mistake: When Ms Botz puts Bart and Lisa on the settee after tying them up, the telephone next to the settee is orange, but in the next shot it is now blue, and when Ms Botz goes to switch on the television, the telephone is orange again.
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