American History X-cellent - S21-E17
Continuity mistake: When Marge is speaking to Bart, Homer comes out of the house with a pumpkin and you can see there is nothing on the doorstep. But when Marge goes to the car, a green doormat has suddenly appeared, and when she leaves, it has gone again.
American History X-cellent - S21-E17
Continuity mistake: When the policeman is speaking to Mr Burns about the stolen artwork, the molding on the door behind Mr Burns changes between shots.
American History X-cellent - S21-E17
Continuity mistake: When Homer (dressed in a knight's costume) is about to hit a book with his weapon at Mr Burns' place, there is a wine bottle beside him that disappears in the next shot.
American History X-cellent - S21-E17
Continuity mistake: When Homer is showing Carl and Lenny the large bottle of wine he has found in the wine cellar, you can see there is nothing on the shield on the label, but when see Homer holding the bottle a few seconds later, the shield has now two lines on it.
American History X-cellent - S21-E17
Continuity mistake: When Homer is powdering his face at the make-up table at the Independence Day Picnic, you can see the door to the wine cellar is open, but in the next shot it is closed.
American History X-cellent - S21-E17
Continuity mistake: When Mr Burns is being served ribs at the Independence Day Picnic, there is a knife and fork by the side of his plate. In the next shot, both items have disappeared.
American History X-cellent - S21-E17
Continuity mistake: When Mr Burns is doing is speech at the conference, the stand initially has nothing on it but later on a microphone appears from nowhere.
American History X-cellent - S21-E17
Continuity mistake: When we see Homer in the audience at the conference at the beginning of the episode, he is sitting between a lady with grey hair and a man with black hair. But when we see a wide view of the audience a little later on, he is now sitting between a man with brown hair and a bald-headed man.
Continuity mistake: When Homer is saying goodbye to Bart at the airport, there is a metal fence behind him that changes position between shots.
Continuity mistake: When Principal Skinner is speaking to Marge and Homer, Homer is lying on the settee and you can see there is nothing beside it, but in the next shot his beer can appears from nowhere.
Continuity mistake: When Principal Skinner rings the doorbell of the Simpsons' house, the handle on the door is pink. But when Marge is at the door, the handle is now light blue.
Continuity mistake: When Principal Skinner and his mother are with Bart and his friends after the toilet prank, you can see Bart has Milhouse, Richard and Lewis are beside him. In one shot, Bart is on his own and the other three boys have gone, and in the next shot, they are back again.
Continuity mistake: When Maya and Moe are at Moe's home, Maya gives Moe a glass of water and he sits down on the sofa with the glass in his left hand. In the next shot, the glass has gone.
Continuity mistake: When Maya and Moe arrive at Moe's house, you can see there is nothing on the arm of the sofa, but in the next shot a remote control appears from nowhere.
Continuity mistake: When Moe is sorting out the flowers at Moe's bar, you can see there is nothing behind the beer taps on the counter, but in the next shot a jar of pickled eggs appears from nowhere.
Continuity mistake: When Maggie is swinging a spade at the other children in the playground, there is a tree behind her that disappears in the next shot.
Continuity mistake: When Homer is pushing Maggie along in her pushchair, Santa's Little Helper comes along and you can see that Maggie has a dummy in her mouth. In the next shot, the dummy has disappeared.
Continuity mistake: At the beginning of the episode, the doormat outside the Simpsons' house is green, but when Maya and Moe arrive at the Simpsons' house for their double date later on, the mat is now purple.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Wiz Kids", when Milhouse is performing his trick at Springwart's Magic Recital, the trick goes wrong and he runs off naked, leaving his cloak on the floor. Later on in the scene, the cloak disappears.
Tree House of Horror XII - S13-E1
Continuity mistake: In "House of Whacks", when Homer attacks the tank, he puts the axe in the right hand side of the tank, but in the next shot the axe is now in the middle of it.
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.
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