Continuity mistake: When Marge runs after Bart because he's hiding something under his jacket, Homer pulls out a gate to block Bart's entrance to the TV room. Three different gate styles are shown. (00:20:35)
Continuity mistake: As Bart is forced to show Marge the item (picture frame) he is hiding, he pulls it out of his jacket and he hands it to Marge. As he pulls it out you can see there is nothing in the frame or on the border of the picture frame. After Marge's reaction to the photo we see a close up of the frame and there is now a picture in the frame and some colorful decorations around the frame. Whilst the frame could have been the backside when he pulled it out he never turned it over when handing it to her, and Marge never turned it around when looking at it.
Team Homer - S7-E12
Continuity mistake: During the classroom scene where Bart reveals his Mad magazine shirt, he removes his sweater and puts it on his desk. In the next shot the sweater disappears. (00:03:40)
Team Homer - S7-E12
Continuity mistake: When Moe says Mr. Burns is going to have an accident, he's wearing his pin pals shirt. When Moe hits Mr. Burns, he wears a mask and different clothes. Moments later, when talking to his bowling team again, he's back in his pin pals shirt.
Continuity mistake: Just before Marge tries to sell Skinner the tie rack, she is writing on something. She then puts her hands down by her waist, and then brings one up to turn it on and both up to pull the motor out. The point is that the pencil and the item she had in her hands have simply vanished, and we never saw her put them down either.
Continuity mistake: When George and Homer burst out of the manhole, there is a shot of the Simpsons' house covered in mud, then a quick one of it totally clean, then another when it's muddy again.
Continuity mistake: When Bart is looking for candy in the cupboards, the wine bottles in the nearby rack change position between shots.
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.
Continuity mistake: At the funeral, while everyone is clapping for Bob Newhart, Mayor Quimby is seen with brown skin.
Continuity mistake: When Lisa first discovers Jebadiah's confession, she is holding the fyffe and wearing his racoon hat, the screen fades to black (I'm guessing for the ad break) but when it comes back Lisa is standing in exactly the same position, still reading the confession, still holding the fyffe, but no longer wearing the hat.
Continuity mistake: When Homer and Lisa are trying to convince The Town board to dig up Jebediah, members of the board keep disappearing.
Continuity mistake: In class, when Lisa is sitting at her desk, pondering the Jebadiah mystery, her tray of cookies and glass of milk is very visible. Then when Lisa says "The missing piece of the puzzle. I've got it." and runs out of class, the cookies and milk are no longer there.
Continuity mistake: The lettering on Smithers' desk name plate changes between shots. While he is taking the call from Mr Burns' mother you can see his name "W. Smithers" in black letters. The shot after seeing Burns, who keeps falling asleep, the letters are now red.
Continuity mistake: When Homer gets up to make Mr. Burns' breakfast, Marge's nightgown is yellow, making her look naked, but in the next shot, her gown is purple.
Continuity mistake: When the first photo is taken of Selma and Troy on their first date, Selma is wearing lipstick. When the photo is published, the photo shows her without lipstick.
Continuity mistake: In the scene where Selma and Troy McLure get caught by the press outside the resturant, Selma and Troy swap places between shots.
Continuity mistake: During the Planet of the Apes musical segment, just before Troy McClure sings "Can I play the piano anymore?", he and Dr. Zaius are standing far apart. In the next shot, they are close together.
Continuity mistake: In the overhead shot of Patty smoking, she is sitting on a greenish-gold car, the car then turns blue in the next shot.
Continuity mistake: After the boy's car gets crushed, Bart sells Milhouse's glasses for $600. Then Milhouse knocks over the Coke bottles and the clerk gets the money back and keeps the glasses. The next scene, where they try to get on a train that goes to Springfield, you can see Milhouse in his glasses and throughout the rest of the episode.
22 Short Films About Springfield - S7-E21
Continuity mistake: When Skinner and the superintendant are having lunch, Skinner brings in four burgers. The superintendant takes one, and suddenly there is only one left.
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