Continuity mistake: When the family are talking and Marge is sitting on the sofa, Bart runs and shoves Lisa (who is in front of Marge) out of the way, but in the next shot, she is still in front of Marge, despite the fact Bart pushed her out of his way.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Wiz Kids", Bart stabs Montymort in his shin which is open (i.e. not covered by what he's wearing). Only a little blood pours out. Then Monty raises his shin into shot and there is not only a puncture in the leg of his clothing, but the wound is covered in blood. When he falls, and Slithers eats him moments later, there is no damage at all. (00:19:55)
Continuity mistake: When Skinner is addressing the class before the meat video we first see him with black trays on the desk to the far right. In the next shot they're much closer to him.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: When the camera pans down the Trade Center, there is no washing line there. But a few shots later, a washing line appears.
Continuity mistake: At the beginning, when there is an overhead shot of the Simpsons' lawn, the broken lawn mower has disappeared. (00:01:20)
Continuity mistake: When Homer is in his mansion watching Weird Al's parody of his song, the trash on his floor (frappuccino cups, pizza boxes, etc.) keeps switching places.
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.
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.
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