Continuity mistake: When Judge Harm is yelling at Marge and Homer after they have cut the rope, Marge is wearing lip gloss, and between two shots, it disappears.
Continuity mistake: When Mr Burns and Homer first enter the cabin, you can see the door opens with a door knob which is on the right hand side (looking from the outside). Later, after the avalanche, the door seems to open a different way, the knob has been replaced by a handle and it's on the other side.
Continuity mistake: Bart flicks through his chequebook in the car and finishes on The Front page of it having gone through all the cheques. When the shot changes he is holding it open.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob come to Quimby's office for the first time, the items on his desk change colour and position.
Three Men and a Comic Book - S2-E21
Continuity mistake: When Martin is tied up in the treehouse, at one point Bart takes the brick off the comic book and sets it down near Martin. When Bart and Millhouse fight, the brick disappears.
Homer Badman - S6-E9
Continuity mistake: When Homer's badly-edited "Rock Bottom" interview is shown on TV, the hands on the clock behind him keep jumping around between all the different cuts. But when we saw him giving the actual interview earlier, the clock behind him stayed at 5 o'clock the whole time. The hands on the clock are also slightly different.
Continuity mistake: Throughout the whole of this episode, the picture keeps on changing on Mr. Burns' wall. Sometimes even in the same scene.
Continuity mistake: Right at the beginning, the first shot of Homer and Lisa shows the door open. After Homer says 'in the most wicked condition' and the shot changes the door is closed.
Two Dozen and One Greyhounds - S6-E20
Continuity mistake: There are twenty-six puppies eating from their bowls in the kitchen. As the title suggests, there's meant to be twenty-five.
Continuity mistake: During the Itchy and Scratchy cartoon, things change about the positions of the cats, the clothing, etc. (00:07:55)
The Call of the Simpsons - S1-E7
Continuity mistake: When the bear first confronts Maggie, she is on a path. Yet in the next shot when the bear lands on the ground, she is on grass. (00:11:15)
Brake My Wife, Please - S14-E20
Continuity mistake: As Hibbert handcuffs Bart to the radiator he uses the second bar to the right. The next shot it's moved to the next bar to the right.
The Old Man and the Lisa - S8-E21
Continuity mistake: Right at the start when Lisa says "I could still use more paper," the plastic can-rings she was holding vanish in the next shot.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When the last wish is granted by Homer, when the index finger moves, you can see the refrigerator to the right of the hand. Homer was standing with his right arm facing the fridge. (00:06:55)
Continuity mistake: When we first see the papers on top of Skinner, the jar of preserves is not visible anywhere. It is beside him in the next shot. (00:19:15)
Continuity mistake: Bart's bruised eye has healed by the time he reaches Skinner's office to lick envelopes. (00:02:40)
Continuity mistake: When Mr. Burns is notified about the Leftorium, the can and can opener have disappeared from Smithers' hands. (00:19:45)
Continuity mistake: When Bart is explained the answer RDRR, there is a shot of him. There is a blue background where the classroom should be.
Continuity mistake: The whole family goes to the opera to see "Carmen". They have balcony seats and the stage is to their left, yet later on you can see them looking to their right.
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Thing and I', at the end everyone is having dinner. Dr. Hibbert says "Care for a drumstick Hugo" and everyone's plate is empty. Seconds later everyone has food without it being served out. (00:06:50)
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