Continuity mistake: When Bart is explained the answer RDRR, there is a shot of him. There is a blue background where the classroom should be.
Continuity mistake: The whole family goes to the opera to see "Carmen". They have balcony seats and the stage is to their left, yet later on you can see them looking to their right.
Deliberate mistake: When Bart is in the genius school, the teacher asks him if he knows what happens if he adds an acid to a base. He replies yes, adds them anyway and the lab explodes and a green goo comes out, turning Bart green. If you add an acid to a base, you just get salt and water.
Continuity mistake: While Bart starts the I.Q. quiz and is reading it out loud, his teacher says "Shh. Visualize it Bart." While this happens if you look in the background you can see the alphabet line. It starts out Tt Uu Vv Ww, then Bart's teacher blocks out some, then you see the letter T again. (00:04:50)
Continuity mistake: When explaining RDRR, Ms. Mellon writes "y=r^3/3" on the board behind her. But after she asks, "Don't you get it, Bart?", the equation disappears from the board and she writes it again.
Continuity mistake: When Skinner is showing Homer the "fake" sick note, the writing is clean and tidy. When we see Skinner comparing the note to the cheque the handwriting is suddenly different. (00:07:15)
Continuity mistake: The writing on the wall changes style and location from when Bart writes it to when Homer walks by. (00:03:00 - 00:06:30)
Continuity mistake: At the start Marge's tiles go from on the table to in her hands when Homer chases Bart. (00:02:55)
Continuity mistake: When Homer chases Bart at the start, the book that Lisa had has disappeared from her hands and she is now holding her tiles. (00:02:50)
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.
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