Continuity mistake: While Homer is sleeping, the fire burns off the hair on his head. But when he wakes up and jumps up off the couch, his hair is back again. (00:17:00)
Continuity mistake: All of the cigarettes that Moe has smoked disappear from the floor after Marge has spoken to him.
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)
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)
Continuity mistake: After the "sponge incident," Bart is standing in the drive with the sponge packet in his hand. In the next shot he says "everything about me must go," but the packet has vanished from his hand.
Realty Bites - S9-E9
Continuity mistake: When Marge finds out the Mr Hutz does real estate, the 'For Sale' sign changes from black to red and then back again.
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the hamster Nibbles has rolled back to Skinner, it takes the lid of the ball off, and the lid lands on the ground. When the hamster is rolling away from Skinner it doesn't put the lid back on, it just leaves it on the ground, but in the next shot the lid is suddenly gone.
Continuity mistake: Just after Homer has used the proton accelerator, Dean talks to him. In this scene he is writing something on a piece of paper, but he writes on the same line every time. He finishes writing on that line, then starts on it again.
Tree House of Horror XII - S13-E1
Continuity mistake: At the end of 'Wiz Kids', when Lord Montymort is defeated, he falls to the floor, breaking all the floorboards. Then when Lisa takes off the headset, all the floor is intact. In the next shot, the floorboards are all broken again. (00:20:05)
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)
Continuity mistake: While Bart is watching wrestling as Marge and Homer are struggling to do the dishes, the buzz cola can he is holding suddenly switches hands between two shots as Lisa is talking to him.
Continuity mistake: In the Itchy and Scratchy cartoon 'A Briss Before Dying', Itchy throws Scratchy's eyes out of the window, but after putting the rest of his body through the grinder the eyes are back.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: At the sale, when Bart and Lisa first find 'The Bee Sharps' album, the order of the records in the stack change in subsequent shots.
Continuity mistake: Just before Bart's flashback, his shirt is orange, and the chair he's sitting on is blue. But in this episode, his shirt is a paler shade of orange and the chairs in the classroom are red.
Continuity mistake: In the scene where Lisa runs into the attic as she dives behind the chest she rattles a bird cage, later when Ned faints you can see that the bird cage has disappeared.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when the machine picks up the Simpsons' house, to take it to the 'Re-Neducation Centre,' the garage is on the wrong side of the house. It is on the correct side in the following shots of Homer returning. (00:11:20)
Continuity mistake: When Lisa knocks Bart's chop out his mouth she knocks it out front, however, the chop ends up going to the far right and into Homer's mouth.
Continuity mistake: When Krusty is sacked, his bottle of pop vanishes. (00:13:45)
Continuity mistake: At the end of the episode when Marge is first seen doing the entertainment, the shot shows (from left to right): Flanders, Skinner, Kirk Van Houten, Kent Brockman, Mayor Quimby, Grandpa, and behind them, Lionel Hutz, Lenny, Homer and Dr Hibbert. In a following shot from behind Marge the guests have changed places. Reverend Lovejoy is on the end, then Flanders, then Skinner, then Mr Burns, then Grandpa. There is a seat next to Grandpa which is blocked by Marge's head. Also Lionel Hutz has moved far back. Where did Burns appear from and where did Kirk, Mayor Quimby, and Kent Brockman all go?
Continuity mistake: In the episode "New Kid on the Block," Bart says his home address is 1094 Evergreen Terrace. In "Homer the Vigilante," his home address is 723 Evergreen Terrace; and for the rest of the series, it has been 742 Evergreen Terrace. (00:18:30)
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