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: 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)
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)
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)
Continuity mistake: When Bart crashes at the social club, his skateboard changes position between shots. (00:05:30)
Continuity mistake: When there is a zoom in of the house just before Bart gets up late, it has the old arch-shaped windows, but in the rest of the episode it has the normal windows. It's obviously a screen from Season 1. (00:06:00)
Continuity mistake: At the end, the barriers outside the tavern change position. (00:21:00)
Continuity mistake: During the Itchy and Scratchy cartoon, things change about the positions of the cats, the clothing, etc. (00:07:55)
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: After Marge says she will marry Homer, at the beginning of the scene, the car is facing the power plant, and at the end, it is facing away from the plant. (00:07:45)
Continuity mistake: When the mobsters enter Skinner's office, the phone on his desk changes position between shots. Also, the name bar on his desk doesn't read anything on it. (00:13:50)
Continuity mistake: In the beginning, when Bart finds that the dog ate his homework, the poster on Bart's door has disappeared for one shot. (00:01:45)
Continuity mistake: When Marge and Homer are arguing about Don Quixote, Marge's pillow disappears from under her head. (00:09:50)
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: 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)
Revealing mistake: When Smithers makes Mr. Burns his Wine Spritzer, Burns makes Homer Employee of the Month. While Smithers is pouring the stuff in the bottle, his left hand turns black for three frames. (00:10:30)
Continuity mistake: When Homer and Barney are talking about the lottery, Barney says, "130 million." Then, they set their mugs on the table but when they all run off their mugs have disappeared. (00:01:50)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: In the parking lot, when Carl arrives, he is wearing a blue tuxedo. It changes to a lighter blue, and then back to its normal color when he gets in the car. (00:07:05)
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