Continuity mistake: This is a mistake for the introduction from seasons 2-20 (1991-2009). When Homer screams, he turns round. You see this in a wide shot. There are no boxes to the right of the door in the garage. However, two just appear out of thin air when he runs through the garage. (00:01:50)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Lewis changes from black to yellow when Milhouse dares Bart to pull Santa's beard off. (00:14:10)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: After Homer brings Santa's Little Helper home, Homer and Marge hug, and if you look behind them, the background is upside down. There is a picture hanging upside down, and there is a lamp which seems to be hanging from the ceiling. Then in the next shot, the background is normal. (00:21:40)
Trivia: Maggie scans as $847.63 in the supermarket at the beginning (not NRA4EVER, as Troy Maclure asserts in 3F31 "The Simpsons 138th Episode Spectacular), the price it costs to feed and care for the average American baby every month.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: While having breakfast, all of the Simpsons' glasses of orange juice keep disappearing and reappearing throughout the scene. (00:05:35)
Continuity mistake: When Bart leaves the school, you can see that his skateboard is green and perfectly flat. But when he is skating through the crowd and past the people at the bus stop, the skateboard has an orange stripe down the middle and is raised at the rear.
Continuity mistake: When Maggie goes through the checkout at the beginning, Marge's trolley is grey and has a red handle. But in the next shot, when Maggie pops out of the bag, the trolley handle is turquoise. (00:00:30)
Continuity mistake: In the introduction, initially Maggie's seat is light purple. However, in the wider shot of her and Marge, the seat changes to a burgundy colour. (00:00:50)
Continuity mistake: In the bit where they sit on the sofa at the start of each episode, there is one rather long one where it starts off with the Simpsons dancing in a line, then gradually evolves into a circus with elephants and men dancing around fire. Look closely in between Homer's right leg and the dancing woman on his right. There is a pile of books on the little shelf underneath the lamp and telephone, and just as the camera starts zooming out from the line of dancing, the orange book on the left noticeably changes to purple. (00:01:20)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer walks out Circus of Values with his purchases, he bumps into Flanders, and all the presents scatter everywhere. Watch out for a red present with a green bow that goes flying near the left hand side of the screen. As soon as it hits the ground it turns into a pink box with a white bow wrapped around it, with no shot changes. (00:10:15)
Continuity mistake: When Martin does his book report, on the blackboard it says 'An afternoon with Ernest Hemingway: Reflections by Martin.' But when Bart goes up to do his report, the blackboard is clean. (00:01:25 - 00:02:20)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: When Marge is speaking on the phone to her sisters, her sisters say something that sounds like they said that Homer is ugly. Marge then puts down the phone wire that she was curling round her finger. You can temporarily see that the phone wire disappears when Marge puts it down. It is at the very end of an early scene, because as soon as this happens it changes to another scene. (00:04:40)
Factual error: After Bart's prank call with Moe, you can see Bart and Lisa laughing. However the telephone's wire does not connect to the receiver. (00:09:40)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Marge walks through the doorway from a room with a piano, beside a bare wall, and on the piano are two frames and music sheets. But when Marge turns the jar upside down, there is a large picture on the wall beside the piano, and the music sheets and frames have disappeared from the piano. (00:08:00)
Continuity mistake: In the new opening credits (from Feb 09) when the camera is zooming into the bullies cutting the head off the statue Ralph Wiggum is nowhere to be seen, but when the head falls off, it lands on Ralph. (00:00:10)
Other mistake: While Homer is in Lisa's bedroom trying to make things right with her, there are three pictures taped to Lisa's mirror. After Homer tells her the music may help, in the next shot Homer walks over to stand behind Lisa. Those pictures taped to Lisa's mirror are weirdly behind Homer's reflection, as if the pictures are taped to the wall behind Homer. Three shots later, when Homer tells Lisa he can fix the dollhouse, his reflection is accurate in relation to those three pictures taped to the mirror. (00:19:20)
Revealing mistake: During the first ten minutes when the twins are explaining to Bart what incompetence means, one of the twins' body disappears, showing a floating head and hair. (00:06:30)
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I": After the kids have found Hugo in the attic, when Marge and Homer return home, both front door knobs (inside and outside) do not have backplates, but once Hugo escapes both door knobs have backplates. The two backplates vanish and reappear repeatedly in following shots. It's funny because when they leave to search for Hugo, Homer shuts the door with no backplates, but then Bart uses a key in the backplate to lock The Front door.
Continuity mistake: Bart's 1st grade drawing of cat on the fridge changes across the episode, especially its ears and whiskers. (00:04:50)
Continuity mistake: In the old main title sequence, when Homer gets out of his car, the door inside the garage is red, but when he is screaming and running towards it, it's now brown. (00:01:40)
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