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
Deliberate mistake: When the giant gold robot picks up the robot containing Homer and shakes him, Maggie suddenly pops up from nowhere and bounces around along with Homer.
Audio problem: When Marge says she wants the padding that goes under rugs her lip movements don't match what she's saying. (00:13:25)
'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.
Continuity mistake: In the scene where Bart is in the Court House, when we first see everyone, on the Judges table there is no gavel, yet when the shot changes, a gavel appears. (00:05:20)
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)
'Tis the Fifteenth Season - S15-E7
Continuity mistake: After the family discover the astrolobe, the gift tag disappears from its wrapping. (00:07:25)
Diatribe of a Mad Housewife - S15-E10
Plot hole: Dr Marvin Monroe says to Marge he was gone for a long time because he was sick. That's impossible because he died in a previous episode and you can even see his tomb in the episode where Maud Flanders dies. [It could be argued that Monroe really was sick. It was never explained how he died and no one mentioned that he really was dead. The grave, the hospital named after him were in the simpsons universe with the belief he was dead. The clip show mentioned his death but alluded any specifics. As Marge mentions she thought he was dead and so could everyone else on the show.]
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 Yet when the shot changes to further away we can see that the pencil has been replaced by a napki, a pot with two pencils has appeared, and the flowers have moved to this side of the table as well.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)
The Fat and the Furriest - S15-E5
Factual error: Homer creates a giant sugar ball by making a normal sized cotton candy on a paper cone, and then coating it with liquid caramel. The cotton candy holds its shape and Homer continues to expand it with more cotton candy and caramel. However, cotton candy dissolves very quickly and tears apart easily. Between the weight and moisture content of the caramel, the original cotton candy would have immediately melted and/or collapsed.
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.
The Ziff Who Came to Dinner - S15-E14
Factual error: When the SEC guys break up the poker game they arm their guns in the same manner you would with a shotgun (there is even the shotgun cocking sound effect) yet they are M-16 style weapons and would not need to be armed this way.
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.
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