Continuity mistake: When Homer and Marge come home from the dinner, Marge is wearing a fancy dress. But when Bart falls out of the house right after Homer walks in, she has her typical green dress on. (00:06:15)
Continuity mistake: When Homer is running down the street with his garbage, it spills out all over the road. But in the next shot when the garbage men are confronting him, all the garbage is gone.
Continuity mistake: When Homer opens up his bar there are 4 cars parked outside, but later when Moe opens the garage door there are no cars, but no one has left.
Continuity mistake: In the garage, Martin walks behind Lewis and the other kid. He jumps to walking in front of them in the next shot. (00:09:05)
Home Sweet Home-Dum-Diddly Doodly - S7-E3
Continuity mistake: At the Flanders' house, in the kitchen, Bart and Lisa have sandwiches on plates in front of them. The shot changes and everyone on the table has an empty bowl including Bart and Lisa.
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: As Bart is on the phone trying to book his new act, you can see there is a split down his white shirt. When the shot changes and he tells Lisa to be quiet you can see that split has disappeared. (00:15:05)
Continuity mistake: After Bart cleans his hands with a cloth after going to the private toilet, he puts it on his shoulder. A couple of shots later it has disappeared.
Continuity mistake: When Selma is on video at the end of the episode, the iguanas's eyes change from yellow to white during the scene, but not between shots.
Continuity mistake: At the end of the episode, Bart is writing lines, and he has already written on one half of the board. On the half he has already written lines on, the lines go down the board about 3/4 of the way, yet when the shot changes, the lines now go all the way down to the bottom of the board. (00:20:35)
Alone Again Natura-Diddly - S11-E14
Continuity mistake: When Homer is filming Ned cutting the bushes between the two front yards, the camera Homer is holding suddenly switches eyes.
Continuity mistake: When Bart is writing from the books in the kitchen, he is seen writing on the paper. In the next shot of him, the paper is clean.
Continuity mistake: In the scene at the beginning when the Simpsons are eating dinner, Marge and Homer's plates are empty, then they have food on them, then they are empty again. (00:03:40 - 00:04:30)
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When Lisa and Marge go on the tour, when the film has finished the woman turns it off with a remote controller and puts it behind her back. In the next shot from behind her it isn't in her hands and there is no sign of a pocket or any indication she put it anywhere else.
Continuity mistake: When Mr. Burns tells Smithers that Homer is the next employee of the month, his huge red chair he was just sitting in has disappeared, and Mr. Burns is in a different position. (00:10:30)
Continuity mistake: When Homer apologizes to Moe at the end, he comes in while the door is left open. It remains closed for the rest of the scene. (00:21:05)
Brother From Another Series - S8-E16
Continuity mistake: When in the dam Bob stops the motors from spinning. Next shot shows the blades spinning again, but when the camera cuts they are stopped again.
Continuity mistake: In the scene where Moe is cleaning his window inside the bar, take notice that the size of the spot he cleans on the inside of the bar is small. But when the shot changes to the outside, with Moe and the others looking out from the inside, the clean spot is larger.
Hello Gutter, Hello Fadder - S11-E6
Continuity mistake: When Homer is talking to Ron Howard on the street, there is no pocket on Homer's shirt. But when he takes the money from Ron, he puts the money in a pocket that suddenly appears.
Moaning Lisa - S1-E6
Continuity mistake: When Marge says, "Oh Homer, you'll lose your head if it wasn't secured to your neck," her necklace is white. However, when she gives the cup cakes to Homer and Bart, it is red. (00:02:00)
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