Treehouse of Horror XV - S16-E1
Continuity mistake: When Lisa goes to see Comic Book Guy, we see that he places the dagger on the table in the centre of the green thing, then when the shot changes and he puts the comic there the dagger is gone. (00:09:45)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Comic Book Guy gets stabbed, we see him reaching for a potion, and in the first shot, its a purple liquid with no label on the bottle, and when the shot changes we see it is a green liquid with a label on the bottle. (00:10:20)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Bart and Lisa go into Mao's, we see above Moe there is a guy wearing a red jacket, then when they're walking past him, he is wearing a light brown jacket. (00:11:00)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Chief Wiggum has been caught, we see him drop his eel pie, then when the shot changes it is not there. (00:13:30)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Chief Wiggum is running for the hot air balloon, you can see in the distance no one is in it, yet when he arrives Professor Frink is in it. (00:13:50)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Professor Frink is showing everyone the giant capsule, in nearly every different shot the colours of the balls change. (00:14:50)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Mr. Burns is lying on the table before the Simpsons enter his body, he is wearing briefs. However, when the Simpsons are inside him, he is wearing boxers. (00:15:55)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Maggie crawls out of the stroller and into the capsule, the stroller has no harness, but when Marge sees the empty stroller, there is a harness.
All's Fair in Oven War - S16-E2
Continuity mistake: Right at the end when James is at the toll booth, we see him wearing a watch on his left hand, then when he's handing the money to the toll booth man, he is not wearing it, then when the shot changes he's wearing it again. (00:20:35)
Sleeping with the Enemy - S16-E3
Continuity mistake: When Lisa is making the game right at the beginning, we see her put a line at the bottom of her one, yet when the shot changes, it is gone. (00:00:25)
Sleeping with the Enemy - S16-E3
Continuity mistake: When looking around the course at the beginning we see there is a spinning toy, which you find in some parks, yet when Willy comes along, it has disappeared in the distance. (00:00:40)
Sleeping with the Enemy - S16-E3
Continuity mistake: When Lisa is talking to Homer at the start, we see that Homer puts his Duff down on the table, yet for the rest of the scene it isn't there. (00:01:15)
Sleeping with the Enemy - S16-E3
Continuity mistake: At the start when Homer is wearing the sweater, when Bart comes in with his test, we see it disappears for one shot, and is then back. (00:02:30)
She Used to Be My Girl - S16-E4
Continuity mistake: Lisa puts a statue of liberty head on it's side in her bed to make it look like she's in bed. But when Marge pulls back the covers the head is face up.
Fat Man and Little Boy - S16-E5
Continuity mistake: When Bart is playing with his toys, we see that in one shot on the shelf there are 4 books, then in the next shot there are 5. (00:03:50)
Fat Man and Little Boy - S16-E5
Continuity mistake: During the scene when the toys are talking about insurance, the design on the arm of the blue jacket changes in different shots. (00:04:00)
Fat Man and Little Boy - S16-E5
Continuity mistake: When Lou and Eddie, the police officers, take Bart's shirts, they both have blue shirts on top, then when the shot changes, one of them has an orange shirt on top. (00:07:40)
Fat Man and Little Boy - S16-E5
Continuity mistake: When Homer goes to see Mr. Gladwell, in one shot, there is no plastic vomit, then a few shots later there is. (00:19:45)
Fat Man and Little Boy - S16-E5
Continuity mistake: In "Fat Man and Little Boy," Homer, while playing with Malibu Stacy, picks up Lisa and runs away from The Front door, which is behind him. In the next shot, however, Homer runs out of The Front door and into the street.
Continuity mistake: When Marge arrives home complaining that she is too tired to talk, there is an alarm clock on Homer's night table. When first shown it is a black electric clock, but when it is shown in the very next scene, it is an old orange one. Only a few seconds passed between these scenes, meaning there was no time for anyone to change it.
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