Continuity mistake: When Barney becomes his old self again at the training center, he gets on a jetpack while holding a bottle. In the next shot while he is in the air, the bottle is gone.
Cape Feare - S5-E2
Continuity mistake: When the Simpsons get out of the car at Terror Lake, there are no rakes on the ground. When Bob gets out of the car, there is a whole stack of them. (00:14:30)
Continuity mistake: When Homer is in Moe's, Moe pours him a full pint. When it's passed to Homer, it's now 3/4 full in the glass. (00:10:40)
Continuity mistake: At the start, Homer has his feet on the floor until Ruth asks for a sander, and one suddenly appears under Homer's feet. (00:02:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, as Bart is being stretchered away, he is sat up on the stretcher, but when Skinner says, "perhaps a life at the mad house..." Bart is now lay down. (00:14:05)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, just as Millhouse is getting ready to move seats, he's sat with his hands in his lap until the shot changes, and then he is holding a red book. (00:12:00)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, the size of the notepad above the phone changes several times. (00:09:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, when Bart gets scared by Homer, there is a spare bowl on the table right next to his. When the shot changes, this spare bowl has disappeared. (00:09:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, Bart throws his spoon when Homer blasts the air horn. When the shot changes, the spoon has reappeared in the bowl. (00:09:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, Bart has a nightmare and walks into the kitchen, and there is no bowl in front of him. When Lisa speaks, a bowl appears in front of Bart. (00:09:10)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: When Homer is being taken to hell, his position in the floor keeps changing. Note the tile patterns. (00:03:40)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: When Homer finishes his donut, the number of bits of paper on the fridge changes from 3 to 4. (00:03:20)
Continuity mistake: When Bart runs his nails down the chalkboard, the image on the board changes slightly; note the legs. There is a gap between one leg and the body in one shot, but not the other. (00:14:00)
Continuity mistake: When reading his responses to college applications, Homer pushes his plate away, but as he stands up, an empty plate appears in front of him. (00:07:00)
Continuity mistake: Homer puts his photo on his application, and there is no white spot behind his head in the picture. When the shot changes, there is now a white patch in the photo. (00:06:00)
Continuity mistake: The writing on the entrance essay Lisa is reading changes between shots. (00:05:40)
Continuity mistake: Burns brings out the mystery box and places it on the desk. This box then simply disappears. (00:03:40)
Cape Feare - S5-E2
Continuity mistake: The design of the wall socket in Itchy and Scratchy changes between shots. Note the screws holding the cover. (00:03:40)
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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