Saddlesore Galactica - S11-E13
Continuity mistake: During the BTO concert, whenever the camera focuses on the crowd, the Simpson family is seen at The Front of the crowd. When the camera focuses on the stage, the Simpsons are at the very back of the crowd.
Like Father, Like Klown - S3-E6
Continuity mistake: When Krusty rings his father, there are glasses on the bedside table. In the next shot they are gone. Meanwhile the other objects on the table have moved around.
Continuity mistake: When we see the wide shot of Sideshow Bob being handcuffed, the reporter standing behind Bart and Lisa is wearing a purple jumper. But in the shot of Bart saying 'Take him away boys', the reporter is wearing a green jumper.
Continuity mistake: When the first photo is taken of Selma and Troy on their first date, Selma is wearing lipstick. When the photo is published, the photo shows her without lipstick.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Marge says, "I wish you wouldn't put Homer down like that.", Patty and Selma's dresses swap colour between shots.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When one of Marge's sisters says, "He blew all your savings on jack o'lanterns.", one of the armrests on the sofa is black for some reason.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer for the second time throws out Patty and Selma, the knocker just stays in the same place as if the door hasn't opened at all. (It looks like it is floating in mid-air).
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: Before Homer sees his vision of Caesar Romero the day sign next to him says 9. After the Duff executives see him talking to nobody they decide to take him away and when they get down there the sign now says 12 with the president of Duff confirming it in his speech. Doubtful it took them 3 days to get down to him and not much reason for Homer to take 3 days off the sign seeing as he was almost passing out from the lack of food.
Continuity mistake: Just before Marge tries to sell Skinner the tie rack, she is writing on something. She then puts her hands down by her waist, and then brings one up to turn it on and both up to pull the motor out. The point is that the pencil and the item she had in her hands have simply vanished, and we never saw her put them down either.
Tree House of Horror VI - S7-E6
Continuity mistake: When Professor Frink is explaining where Homer is, in "Homer3", Ned Flanders is leaning behind the couch between Bart and Marge, and Chief Wiggum is standing up. When Homer complains, Ned is between Marge and Chief Wiggum, who is now sitting down on the couch.
Continuity mistake: When Santa's Little Helper is taken away by the Repo Men, the van's back bumper is first seen to have no number plate. When the van drives off, there is a number plate.
Tree House of Horror VI - S7-E6
Continuity mistake: For most of "Homer3", Marge's shoes are red. When Frink explains that Homer is 3rd Dimension, Chief Wiggum says, "Slow down, egghead". During this shot, Marge's shoes are green. When Homer complains, Marge's shoes are back to red. (00:18:05)
Continuity mistake: When Lisa is interviewing people for her newspaper articles, the order is Nelson, Ralph and then the two purple twins, Sherry and Terrie. But after Ralph has been seen, it is not the twins but a totally different person, Lewis. (00:07:30)
Continuity mistake: When Lisa is first delivering her newspaper, Red Dress Press, she unties a pile and the strings are untied. Then the shot changes and the pile has been done up instantly. (00:05:55)
Radio Bart - S3-E13
Continuity mistake: When Marge puts Maggie to bed, her pacifier changes from red to light brown between shots. (00:08:10)
Days of Wine and D'Oh'ses - S11-E18
Continuity mistake: The police car door doesn't appear on Barney's arm until they watch the video.
Continuity mistake: As Martin reveals his Honor Rollor at the time trials, we can see Bart on the right side of the screen. He suddenly appears beside his car in the next shot. (00:13:00)
Lisa's Pony - S3-E8
Continuity mistake: At the end, the melted cheese and work outfit disappears from Apu's hands. (00:21:20)
Lisa's Pony - S3-E8
Continuity mistake: In the kitchen, there is a clock on the wall that changes time from 07:10 to 09:10. (00:12:10)
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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