Continuity mistake: When Martin does his book report, on the blackboard it says 'An afternoon with Ernest Hemingway: Reflections by Martin.' But when Bart goes up to do his report, the blackboard is clean. (00:01:25 - 00:02:20)
Continuity mistake: Bart's 1st grade drawing of cat on the fridge changes across the episode, especially its ears and whiskers. (00:04:50)
Continuity mistake: When Bart hands Ms.Krabbappel his final test, there are some shots going back and forth between their faces. During the first shot looking at Ms.Krabbappel, you can see a window behind her, and outside the window, there is no snow, even though there was a whole lot of it yesterday. During the next shot, the snow IS there. As the camera goes back and forth, the snow disappears and reappears.
Continuity mistake: When there is a zoom in of the house just before Bart gets up late, it has the old arch-shaped windows, but in the rest of the episode it has the normal windows. It's obviously a screen from Season 1. (00:06:00)
Continuity mistake: Just before Bart's flashback, his shirt is orange, and the chair he's sitting on is blue. But in this episode, his shirt is a paler shade of orange and the chairs in the classroom are red.
Continuity mistake: When Lisa shows her exam to her family, the "a" note keeps changing from being circled in red and in a red round. (00:04:30)
Continuity mistake: When Bart gets off the bus there is a fire hydrant behind him. When we see the bus drive off the hydrant has gone. (00:07:10)
Continuity mistake: When Bart gets on the bus the day of the test, Milhouse is sitting at The Front of the bus. When we see Sherri and Terri looking at Bart, Milhouse has gone. (00:06:30)
Continuity mistake: When we see the big ape on the TV, the people running keep changing colour from black to white. (00:05:00)
Continuity mistake: When Homer puts Lisa's test on the fridge, a lot more papers appear on the fridge. (00:04:50)
Continuity mistake: The door to Mrs. Krabappel's classroom has a window, but when Bart fakes being sick then walks out of the class (we see the desks as the door closes), the door's window has vanished, and the doorknob has switched sides as well. Additionally, earlier, when Bart deliberately falls off his chair in class, note that one of the bars on the back of his chair has gone missing. (00:07:35)
Continuity mistake: After Mrs. Krabappel asks Bart to name the pirate in Treasure Island, when it cuts to a closeup of Bart we see the set of blue books have vanished from Mrs. Krabappel's desk, and a Krusty mug has suddenly appeared there. (00:03:00)
Continuity mistake: When Bart fails the test despite having actually studied, we see the two red "X" marks in the center row of the multiple choice questions, but after Mrs. Krabappel passes Bart because he applied practical knowledge, when Homer hangs the test up on the fridge those two "X" marks in the center have vanished.
Continuity mistake: Bart's bedroom is on the opposite side of the stairs, with his window facing out to the backyard, but after his prayer his bedroom window is facing The Front of the house. Additionally, the style of his window changes as well, going from two horizontal sliding panes with no muntins, to a vertical sliding window with two muntins when Marge pulls the curtain back, then to a having only one muntin when Bart opens his window.
Continuity mistake: When Bart is called up to give his oral book report keep your eye on Bart's book, Treasure Island, and the direction of its binding. The book's binding should be to the left of The Front cover, which has the picture of a pirate wearing a black hat, but the binding changes to the right side (note the cover picture/title) of the cover at times, and when he mentions the publisher the book also changes how it's held by Bart. (00:02:10)
Continuity mistake: The colour of the school changes from yellow when Martin and Bart are talking before the test to grey when Bart has spoken to Otto about being held back. (00:07:00 - 00:11:00)
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