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)
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 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: At the start Marge's tiles go from on the table to in her hands when Homer chases Bart. (00:02:55)
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: 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: 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 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: When the teacher is looking out of the window, Bart has his paper in front of him on the desk. The paper disappears in the next shot, but reappears when Bart takes Martin's paper off the table and puts it on his desk. (00:06:10)
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 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: 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 Homer talks to Bart about ties, the two strands of hair on top of his head are missing. (00:09:20)
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: 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 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.
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