Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Thing and I' Dr. Hibbert is about to explain Bart's irregular birth. In the closeup before the story, Dr. Hibbert has a stethoscope around his neck. This wasn't there in previous shots. (00:03:50)
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)
Continuity mistake: At the Institute, the clipboard Dave is holding repeatedly switches arms between shots. It also disappears entirely. (00:09:35 - 00:10:35)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Samantha is being introduced to the class, there is a boy in The Front row on the right side that is wearing a white shirt and has brown hair. A few shots later (an overhead shot of the classroom), the boy is completely different, with a blue shirt and white hair. (00:04:00)
Continuity mistake: Near the end of the episode, when Skinner shouts at Ralph to shut up, the sky outside the bus changes from nighttime to daytime between shots. (00:14:15)
Homer Badman - S6-E9
Continuity mistake: After Marge's left pocket rips in the candy convention, she goes to start picking up the candy when we see that the right pocket has ripped all of a sudden. When Homer and Marge start running away the pockets are no longer ripped and full of candy again.
Springfield Connection - S6-E23
Continuity mistake: Before Marge sees Homer parking violation, if you look at where he is parked over the first handicapped spot there is a car parked in the first non-handicapped spot. A bit before Marge arrests him there is now a non-handicapped spot between the car and Homer's car. (00:14:35 - 00:15:05)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: When Homer makes the food with the mix of Tom Collins mix, cloves and a pie crust you can see the labels on the Tom Collins mix and the cloves change between mixing the ingredients and after tasting them. Also the top on the Cloves bottle keeps changing through the scene. When Homer takes the bottle out of the fridge you can see a red top on it. When he sits down the top has disappeared and starts pouring the cloves. When the shot changes the red top is back and it disappears after that. (00:15:20)
Continuity mistake: When Nelson asks Bart what song he is playing as they wait for the bus, Nelson's vest is orange and his shirt is bluish. However, when the bus arrives and Nelson goes to get on the bus his vest is now bluish and his shirt orange. (00:10:10)
Tree House of Horror VI - S7-E6
Continuity mistake: During the 'Nightmare on Evergreen Terrace' segment, when Bart is running from Willie, he plans to sink Willie in the sandbox. In the first view of the sandbox it is isolated on a field, yet when Willie is sinking in the sand there is a jungle-gym beside the sandbox. (00:11:35)
Continuity mistake: As Bart is forced to show Marge the item (picture frame) he is hiding, he pulls it out of his jacket and he hands it to Marge. As he pulls it out you can see there is nothing in the frame or on the border of the picture frame. After Marge's reaction to the photo we see a close up of the frame and there is now a picture in the frame and some colorful decorations around the frame. Whilst the frame could have been the backside when he pulled it out he never turned it over when handing it to her, and Marge never turned it around when looking at it.
Continuity mistake: When it is announced that Amber is the winner of the contest, and Lisa is runner-up, the stands in the back of the stage are empty. However, when Lisa walks off, all the contestants are back on the stands. (00:15:00)
Tree House of Horror XII - S13-E1
Continuity mistake: At the end of 'Hex and the City,' there is a shot of the wedding cake, then it pans across the people at the wedding, and you can see Homer with his white shirt on. But then when it goes to a closeup, he suddenly has a blue suit and tie on. (00:06:45 - 00:07:20)
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the Hamster rolls through the glass of Flanders car it breaks it near the bottom middle of The Front windshield. Later on when Flanders and Homer are taking the kids home you can see the break in the glass has now moved to about halfway up The Front windshield. On of the following shots it moves back to its original position and then moves back to being around the middle of the windshield.
Continuity mistake: The colour of the alien poster in the nerds' room changes from pink to blue.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: After Maggie makes her wish, the family jumps from being in their seats to beside the window. (00:03:50)
Continuity mistake: At the beginning, when we see the exterior shot of the bus, it is full of kids. In the interior shots, 1) before the twins talk to Bart and Milhouse, every seat is empty, even Sherri and Terri's. 2) when the bus arrives at the school, we AGAIN see a full busload of kids. (00:01:30 - 00:02:25)
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)
Continuity mistake: Patty sprays Barney with pepper spray. It disappears from her hand in the next shot. (00:18:55)
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