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: At the "Do What You Feel" Festival, Homer shows up in his house robe, bear feet styled slippers, unshaven, and unbrushed hair. When he takes the float to save Bart, he's in his regular clothing of blue pants, white shirt, shoes, and clean shaven.
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.
Continuity mistake: When Cesar and Ugolin are eating their lunch, Ugolin's dish only has some potatoes in it. A few seconds later, the dish now has two sausages added to it.
Continuity mistake: When we see Lisa eating her dinner, she has a glass of water by her plate. But when we see a full view of the table, the glass has gone.
Continuity mistake: When Adil is speaking to Lisa at dinner at the Simpsons' house, Lisa has a knife and spoon by the side of her dish. In the next shot, both items have disappeared.
Continuity mistake: When Bart is sitting in the bike passenger seat on his way to the Chateau Maison in France, you can see the seat is coloured brown, but when he arrives at the Chateau, the seat is now blue.
American History X-cellent - S21-E17
Continuity mistake: When Homer, Carl and Lenny are drinking at Moe's Tavern, Smithers' bottle in front of them on the table changes position 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