Radio Bart - S3-E13
Continuity mistake: When Homer, Marge and Sting are down the hole and Sting is digging, Homer is wearing a vest. But in the next shot when they find Bart and Homer moves Sting out of the way, he is wearing a shirt. (00:20:50)
Continuity mistake: At the start, the remote on the sofa next to Homer simply vanishes and returns when Marge walks in. (00:00:40)
Continuity mistake: When Homer is eating the snacks at the start, he drips some dip on the sofa that vanishes when Marge appears. (00:00:50)
Continuity mistake: At the start, the design on Homer's beer can change. Note the white stripe. (00:00:55)
Continuity mistake: When Homer gets off the phone to Moe, all the snacks he had have simply gone beyond a few remaining bits. (00:02:00)
Continuity mistake: When Homer is yelling at the TV about being wrong 48% of the time, the colours of his beer can are reversed. (00:03:40)
Continuity mistake: When Lisa is lying on the floor, she has 3 pieces of paper/notepads with her. Once she starts to ring Moe though, there are only 2 pieces of paper on the floor. (00:12:05)
Continuity mistake: Just as Barney asks Homer if he wants to go bowling next Sunday, Moe's boot disappears from the bar and the money appears in Homer's hands off the bar. (00:12:20)
Continuity mistake: When Homer goes to apologise to Lisa, he walks into her room and leaves the door open. As he steps inside however the door is now closed. (00:15:50)
Continuity mistake: Homer picks up Lisa who puts her Malibu Stacey down on the bed. When Homer puts her down, the doll and house have disappeared. (00:16:30)
Continuity mistake: At the bar when Homer is watching the superbowl, his hands keep changing position between the shots. (00:19:00)
Continuity mistake: Homer goes to ring the phone number '1-909-WIN-BIGG' but we see he only presses four dials, and that's all we hear too.
Homer Alone - S3-E15
Continuity mistake: In the scene where Maggie rips of the top of her bottle, the milk spills everywhere, including on Marge's face. After this Marge goes really crazy and starts screaming. Right before she does this the milk on her face disappears. (00:04:50)
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)
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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