'Tis the Fifteenth Season - S15-E7
Continuity mistake: After the family discover the astrolobe, the gift tag disappears from its wrapping. (00:07:25)
Continuity mistake: When Lisa is helpfully explaining what a Bar Mitzvah is, Krusty's new puppy loses its red lead. (00:07:30)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: When Marge is typing her novel on the computer, in one close-up shot of her we see there is a pencil on one side of the table and a pot of flowers on the other. Yet when the shot changes to further away we can see that the pencil has been replaced by a napki, a pot with two pencils has appeared, and the flowers have moved to this side of the table as well. (00:06:20)
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: When Bart and Milhouse arrive at Milhouse's home, there is a red car in the driveway. When Bart screams, it has gone. (00:05:10)
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When Homer sneaks into Maggie's room to smash the CD player, there is a yellow box with musical notes painted on it. The notes are different in each shot. (00:02:30)
Catch 'em If You Can - S15-E18
Continuity mistake: When Bart, Lisa, Homer and Marge are on the ferris wheel near the end, we can see in one shot the person behind Lisa has blonde hair, and then in the next shot the person has black. (00:18:45)
Continuity mistake: While Krusty is describing his prostate to the children, the green umbrella vanishes from beside Lisa. (00:07:40)
Catch 'em If You Can - S15-E18
Continuity mistake: The Credit card numbers for Ned and Rod's VIZA cards are exactly the same: 8525 4941 2525 4158 First Bank of Springfield Viza valid from 1/1 to 12/31(thirty years on the credit card?)
Catch 'em If You Can - S15-E18
Continuity mistake: When Homer and Marge think they have finally got away from Bart and Lisa and Homer is about to look in the dinner bowl, on the table holding the food there is a bottle of champagne and two glasses, yet when Bart and Lisa jump out the 3 things have vanished. (00:17:20)
The President Wore Pearls - S15-E3
Continuity mistake: When Lisa goes into Principle Skinner's office to resign, there is a mug and some papers on the desk. When she wants to use the microphone, the desk is clear.
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: Right at the end Lisa is holding a doll head and some cards. There is a very brief shot of Bart, and then when it's back on Lisa she doesn't have anything in her hands when they hug. There wasn't time for them to be put down and you cannot see them anywhere either.
Continuity mistake: The Simpsons' bathroom has changed position. In 'Today I am Klown' it was opposite the top of the stairs, at the back of the house; in this episode it is at The Front of the house. (00:00:35)
Continuity mistake: When Krusty ends up at his old neighbourhood, the street changes between shots. E.g. the "LLBeanie" sign appears above the door of the 2nd shop and the suit of the man reading the newspaper changes from grey to blue. (00:05:25)
Continuity mistake: After he takes a puppy from Bart, Snake's car appears from nowhere. (00:04:15)
Continuity mistake: Right at the very end scene, when Lisa and Maggie are sitting on the bed, you can see that there are 6 bricks on the bed. Yet when the shot changes there is only one behind Maggie, meaning two of them have just vanished. (00:20:30)
The Ziff Who Came to Dinner - S15-E14
Continuity mistake: In once scene, Artie walks past the Simpson's to Selma (or Patty). In the next shot he is shown walking past the Simpson's again.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: At one point in the cycle shop, Homer has his hand in his pocket in one shot, and it's suddenly out in the next one.
Margical History Tour - S15-E11
Continuity mistake: Lisa empties a glass of red wine that she previously poisoned with sleeping potion. When she falls over sound asleep, her glass is shown on the ground next to spilled wine.
Continuity mistake: When Lisa is explaining to Marge why she is unhappy, the door to her bedroom closes on its own. (00:07:10)
The Ziff Who Came to Dinner - S15-E14
Continuity mistake: When the Simpsons first see Artie Ziff in the attic, as he stands up, there's a theremin behind him (corresponding with Homer's comment that the "ghost" was playing his theremin). Artie puts a sign up above it. However, when Artie moves to the rafters, the sign he put up is still there, but the theremin isn't.
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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