Some Enchanted Evening - S1-E13
Continuity mistake: When Homer and Marge leave the house for the evening, there is initially nothing by the doormat when they leave, but in the next shot two pink cases suddenly appear.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer is putting the shaving foam on his face in the bathroom, he initially puts the can on the left hand side of the shelf, but in the next shot it is near the mirror.
Some Enchanted Evening - S1-E13
Continuity mistake: Before Homer is about to enter the house, the handle is on the left hand side of the door, but a few seconds later the handle is now on the right, and when Marge opens the door, it is back on the left again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer is speaking to a customer at Moe's Tavern, the customer has a bowl of peanuts in front of him, but in the next shot the bowl disappears.
Some Enchanted Evening - S1-E13
Continuity mistake: When Marge is speaking to Dr. Monroe on the telephone, the doughnuts in the box next to him change between shots.
Some Enchanted Evening - S1-E13
Continuity mistake: When we see a full view of the kitchen after Homer, Bart and Lisa have left, you can see there is a toaster on the sideboard behind Marge, but in the next shot there is now a radio behind her.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer is eating his breakfast at the start of the episode, there is some green food with his bacon and egg. But when the doughnut lands on his plate there is no green food, and when he is eating the doughnut, the green food is back again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Bart is eating his breakfast at the start of the episode, there is a knife under his arm. The knife disappears in the next shot, and in the shot after that, it is back again.
Some Enchanted Evening - S1-E13
Continuity mistake: During the breakfast scene at the start of the episode, the milk carton holder is initially blue but changes to white in the next shot.
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: 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: 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 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: 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 Homer puts Lisa's test on the fridge, a lot more papers appear on the fridge. (00:04:50)
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 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: 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: 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)
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)
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