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.
Continuity mistake: When Bart and the three other boys are standing by the wall after Bart sprayed a drawing of Principal Skinner, there are bushes by the end of the wall. But when we see Martin standing by the drawing, there are no bushes.
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: 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 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)
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer gives Ms Botz her money when she is in her car, she takes it but in the next shot the money is nowhere to be seen.
Some Enchanted Evening - S1-E13
Continuity mistake: When Ms Botz puts Bart and Lisa on the settee after tying them up, the telephone next to the settee is orange, but in the next shot it is now blue, and when Ms Botz goes to switch on the television, the telephone is orange again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer pours Marge some champagne in the restaurant, you can see there is nothing by the side of Marge's plate. In the next shot, a knife suddenly appears, and in the shot after that, it is gone again.
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 Bart is standing under the shelter of "Bon Dormir", the pavement on which he is standing is grey. But when he is talking to a policeman, the pavement is now a more darker grey.
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