Homer Alone - S3-E15
Deliberate mistake: Arnie says that he drops his bagel. When he does he starts to say it, but when we see the helicopter it has just fallen out. If he dropped it at the time he did, then it would be much further down and wouldn't be visible in that shot. (00:05:20)
Homer Alone - S3-E15
Continuity mistake: In the scene Marge goes crazy in the car, Homer is let through, and he passes under 'distressed mother' police tape, but in the next shot, the tape has disappeared. (00:06:40)
Homer Alone - S3-E15
Continuity mistake: When Barney is kneeling by The Front door step, a pool of water appears next to him instantly. (00:16:40)
Homer Alone - S3-E15
Continuity mistake: When Marge has finished the list of things to do at Rancho Relaxo she has a list on the bed. When we next see Marge a few seconds later, the paper is gone. (00:17:50)
Continuity mistake: When Bart writes the first letter as Woodrow, he writes it on lined paper. However the letter Edna reads is on plain paper. (00:07:30)
Continuity mistake: The letter Bart receives from Edna reads "94 Evergreen Terrace," however in other episodes they live at 742 Evergreen Terrace. (00:08:45)
Continuity mistake: The photo Edna sends to Bart differs when he shows his parents. The angle is different from what it was previously, revealing part of a photo frame on the wall which wasn't there before, and the sheets/pillows on the bed are different, and her eyes are closed when they look at it, but when Bart looked at it, they were open. (00:09:05 - 00:18:25)
Continuity mistake: When Edna waits in The Gilded Truffle, she checks her watch. In the next shot the watch has gone. (00:15:40)
Continuity mistake: When Edna sits at her desk saying "Oh, Woodrow. How could you stand me up?" the clock reads 3 O'clock. Seconds later, as Bart talks with Edna, the clock reads 4 O'clock. (00:16:45)
Continuity mistake: When Homer stands on the nail in the back yard, you can see behind him, that on the wall next to the back door there are two purple lights. Seconds later when Lisa shows him the new doghouse, the lights have gone. (00:17:25)
Continuity mistake: The notepad Homer draws the blueprint on changes from having content on it to being blank so he can draw on it.
Continuity mistake: The waiter at The Gilded Truffle who takes the chair away turns into a completely different waiter when the angle changes.
Other mistake: Marcia Wallace is credited as a special guest voice even though Mrs. Krabappel's role was cut. (00:29:00)
Continuity mistake: When Burns first shows the team the nerve tonic, the "&" on the 'Brain & Nerve Tonic' label is facing backward, but as Burns pulls it away it faces forward. Then as he moves it around as he's talking, the "&" switches between facing forward and facing backward again. This happens all in the one shot.
Audio problem: When we see Steve Sax driving, he says "What a nice little town" but his lips don't move.
Continuity mistake: At the beginning of the episode, the school is a light purple colour, yet near the middle of the episode, the school turns yellow. (00:00:50 - 00:12:20)
Continuity mistake: In the scene at the beginning when the Simpsons are eating dinner, Marge and Homer's plates are empty, then they have food on them, then they are empty again. (00:03:40 - 00:04:30)
Continuity mistake: Near the beginning when the family is eating dinner, the glasses on the table keep refilling/emptying themselves, even though nobody takes a drink. (00:03:40 - 00:04:30)
Continuity mistake: At Li'l Ludwig's Music School, when Lisa plays her sax she has a rope around her neck, attached to the sax. Then when Lisa yells "You're wrong. You're wrong." The rope has vanished, but is around her neck in the following closeup. (00:05:05)
Continuity mistake: When Lou and Eddie (the police officers) arrive at the house to take Bart for a drive, their badges are white. When they are driving in the cop car, their badges are yellow. (00:05:30)
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