'Tis the Fifteenth Season - S15-E7
Continuity mistake: After Homer decides that he doesn't want to sleep with Marge, he goes downstairs and watches TV. He moves to a different side of the sofa between shots.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: In the bathroom, Lisa can't stand the Roofi CD being played so she pulls the plug out of the plug socket to stop the radio playing. In the next shot, the plug has disappeared from the radio. (00:02:15)
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)
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When Bart asks Ms. Krabapple for detention, the piece of paper on his desk disappears. (00:03:05)
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When we see The Town at the meeting, Smithers is sitting in front of Selma. In the next shot, though, Smithers is suddenly on stage holding the 'SSCCATAGAPP' sign and Lenny is sitting in front of Selma. (00:08:50)
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When Roofi is singing at the concert, the Roofi head on the curtain is facing the left. Later, it is facing the right.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: When the boys get to the top of the hill the light on The Front of the bike has shrunk dramatically since the first time we saw it at Bart's driveway. (00:00:55 - 00:02:15)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The cats' graves change position. When Snowball II is buried, they're away from the the tree and near the fence. When Snowball III is buried, the graves are away from the fence and Snowball is among the roots of the tree. (00:04:10 - 00:09:25)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The remote control for the robot in Bart's bedroom appears from nowhere. (00:08:30)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: When Snowball III drowns, the number of weeds and rocks in the fishtank changes between shots. (00:09:15)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: When the family are eating dinner after the robot fight, their water glasses change position between shots. (00:12:40)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The jagged piece of metal that Homer pulls from his arm disappears from the bedside table in the very next shot. (00:16:30)
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.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: In this episode it is shown that Snowball I is buried in their backyard, but in other episodes, notable the one where Sideshow Bob becomes mayor, it is established that she is buried in a pet cemetary.
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: Right at the beginning of this episode, Homer is wearing a watch on his left hand, and he is still wearing it in one shot when he's in the car, but when he reclines his chair it is gone. (00:00:30)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: When we first see the book-reading Ms.Krabbapple is sitting at the end of the row. The next time, Groundskeeper Willie is there. And the third time we see the audience, Apu has appeared in The Front row as well. (00:02:25)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: When Homer comes home in the Ambulance we can see there is a yellow logo on the back passenger door. In one shot it randomly disappears. (00:05:40)
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)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: At the book signing, Dr Marvin Monroe is significantly slimmer when seen from behind than when see from in front. (00:14:50)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: During the "performance" at the end of Marge's book, "Ned" is skewered by a harpoon and falls off the cliff. When "Homer" walks up to the cliff edge you can no longer see the rope trailing from the end of the harpoon. However, moments later he gets his leg caught up in it and is pulled over himself.
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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