Continuity mistake: If you watch carefully, the same footage of Bart and Skinner slamming locker doors is used. The easiest to spot is the shots of the camera at Bart from inside a locker, where a kid's scrapbook is on the left side. (00:19:45)
Continuity mistake: When Marge is talking to Lisa in her room about Band Practice, Lisa is reading comics, eating potato chips, and there is a drink by her as well. The drink container starts out green with a light purple label, then goes to being grey with a red label then as Marge tells her story, the colours of the drink change again twice. (00:10:00 - 00:10:55)
Continuity mistake: At the beginning of the episode, the school is a light purple colour, yet near the middle of the episode, the school turns yellow. (00:00:50 - 00:12:20)
Continuity mistake: When Lou and Eddie (the police officers) arrive at the house to take Bart for a drive, their badges are white. When they are driving in the cop car, their badges are yellow. (00:05:30)
Audio problem: When Eddie and Lou are taking Bart for a ride in a police car, Eddie says "I tell you, they only come out at night" the audio does not match what he is saying. (00:06:10)
Revealing mistake: When Lisa is clapping erasers, you can see the alphabet above the board, and part of the A is cut off.
Continuity mistake: When Lisa is clapping erasers because she sassed Miss Hoover a second time, the room's clock is visible near the top of the ceiling. However, the clock wasn't there several shots earlier. (00:17:00)
Continuity mistake: When Lisa decides to take Miss Hoover's Teacher's Edition, we see "Teacher's Edition" on the spine of the book. But when Lisa puts it in her bag the spine of the book is completely blank.
Continuity mistake: When Millhouse spits the paper at Kearney in the cafeteria, Jimbo is seen wearing a black shirt and Dolph is wearing a green shirt yet, when Millhouse is dragged out the cafeteria by Bart, they are both wearing blue shirts. (00:16:10)
Continuity mistake: When Chief Wiggum says, "Give him your badge," he doesn't have anything on the right side (his right) of his shirt. After the camera flashes to Bart and back, Wiggum suddenly has a badge there.
Revealing mistake: After Bart gets promoted to Hall Monitor, when he tells the girl at the fountain to keep the line moving, the kid behind her drinks from the fountain but the water does not go into his mouth. (00:13:40)
Continuity mistake: After Bart finds out that Lisa took the teacher's books, his Hall Monitor sash disappears and reappears for several shots. (00:20:05)
Continuity mistake: When Bart uncovers the photo of the Simpsons behind the books in Lisa's locker, the books change between shots.
Continuity mistake: When Bart and Skinner are checking lockers, you can see in a wide shot that Bart needs to check seven lockers before he gets to Lisa's locker. However, Bart checks eight lockers and then opens Lisa's locker. (00:19:35)
Continuity mistake: In the cafeteria scene where Milhouse shoots a spitball at Kearney, in the shot when Milhouse says, "We have order, but at what price," Milhouse, Lewis and the bullies all change positions at their tables. You may have to watch this part several times to understand it. (00:16:45)
Continuity mistake: After Bart cleans his hands with a cloth after going to the private toilet, he puts it on his shoulder. A couple of shots later it has disappeared.
Continuity mistake: At the end of the episode, Bart is writing lines, and he has already written on one half of the board. On the half he has already written lines on, the lines go down the board about 3/4 of the way, yet when the shot changes, the lines now go all the way down to the bottom of the board. (00:20:35)
Continuity mistake: In the scene at the beginning when the Simpsons are eating dinner, Marge and Homer's plates are empty, then they have food on them, then they are empty again. (00:03:40 - 00:04:30)
Other mistake: When the pupils are doing the test at school, you hear Miss Hoover say a question with three possible answers; but 1) There are 5 possible answers on the test when we see Lisa doing it, and 2) Miss Hoover says the 60th question, but Lisa looks to be nowhere near the 60th question.
Continuity mistake: At Li'l Ludwig's Music School, when Lisa plays her sax she has a rope around her neck, attached to the sax. Then when Lisa yells "You're wrong. You're wrong." The rope has vanished, but is around her neck in the following closeup. (00:05:05)
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