Continuity mistake: In the shower scene, we see that in front of Carl, there is a man with brown hair and a moustache in front of him, but then when the shot changes, the man has moved cubicles and a man with white hair has taken his place, and he wasn't even in the previous shot. (00:14:50)
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: Right at the beginning of the episode when all the children are on the bus we can see that in front of Nelson is Bart and behind him are Lewis, Martin and Wendall. Then when the shot changes to behind Nelson, Lewis has swapped places with Bart, Bart has disappeared and some weird kid is sitting where Lewis was. (00:00:40)
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)
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
Audio problem: After watching 'Robot Rumble', Bart tries to dissuade Homer from building a robot by listing his other "talents". The voice and Bart's mouth movements don't at all match. (00:06:20)
Margical History Tour - S15-E11
Continuity mistake: In the Mozart sketch, the music Bart writes with his foot and then picks up suddenly vanishes in the next shot.
Continuity mistake: At the Randall Curtis's Ranch we see Randall Curtis ride off on a Ton-Ton to go to the video store but in a scene only a few minutes later we see Marge and Homer drunk, tossing him around. Unless the video store is on the ranch or very close by this doesn't seem possible for someone so determined to rent movies.
Continuity mistake: When Homer and Bart are fighting in the bathroom, in one shot we see the shower knock some bottles from the shelf on the wall, but then straight in the next shot they're back on the wall. (00:00:50)
Continuity mistake: Lisa's Malibu Stacy dollhouse disappears from the rug after Maggie spells 'price' with her blocks. (00:03:55)
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)
Continuity mistake: When Marge is saying she would never have married Homer if she had known it was him in the camp, she is on the couch. But in the next shot, Marge is standing up and the cat and dog are on the couch.
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)
Catch 'em If You Can - S15-E18
Factual error: Bart gets bored of "Love Story" and presses the split-screen button to watch Krusty, which replaces the movie audio with the Krusty audio. Split-screen buttons only provide a picture, not an audio.
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: At the beginning, when Nelson is describing his family problems to the bus, the children change position between shots. Watch, for example, the boy sitting in front of Martin; in some shots he is white, in others black. (00:00:30)
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)
Continuity mistake: During the 'whose garter is this?' joke Patty and Selma appear behind the Simpsons. (00:20:10)
The Fat and the Furriest - S15-E5
Continuity mistake: When Homer realises that the bear was only agressive because of the electrical tag, they share a bear hug. The back of Homer's shirt is torn to tatters, and his back is bleeding. Immediately thereafter, the back of Homer's shirt is completely intact.
The President Wore Pearls - S15-E3
Continuity mistake: At the end of the episode Lisa gets on the school bus and in the back of the bus there is an emergency door with a small window in it. The following shot she starts singing out the back of the bus but the window has disappeared.
Treehouse of Horror XIV - S15-E1
Continuity mistake: After Homer tries to stab himself with the banana, he drops it. But when Nelson's clothes disappear, the banana has vanished.
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: Milhouse is holding the Monopoly set in the Simpsons house. Then when his Dad comes in he isn't. Granted he could have put it down, but it isn't anywhere we can see, so he would have had to put it down behind the sofa which is somewhat unlikely.
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