Continuity mistake: When Agnes meets Bart and his friend, it cuts to Skinner, then to Bart's group and quickly back to Skinner. When it goes to Bart's group (before Skinner) Lewis is yellow like the rest, in all other scenes he is black.
Continuity mistake: Just before Lisa's Presidential "refund adjustment" speech she pushes Bart's tape player off the desk and we can hear it smash off screen. Later in the episode when Lisa agrees to legalise it, he starts playing the same player.
Continuity mistake: During The Town hall scene, Ruth Powers (the woman with the red bandana) is seen with blondish hair in two shots. All other shots of her during this scene shows her with her usual brown hair.
Continuity mistake: When the women of the neighbourhood throw Marge a baby shower because she's pregnant with Maggie, Ruth Powers is one of the ladies there. Ruth only met Marge when she moved to Springfield with her daughter in "New Kid on the Block" (Maggie was already born in the episode).
Continuity mistake: When Marge spots Krusty, from the regular view, Krusty's hand is down on the table. But from the view from the camcorder, his hand is on top of the cake. (00:14:00)
Continuity mistake: When we see Marge leave Bart with Patty and Selma, they are stood with a gap between them. Camera changes to focus on the sisters, and they are now next to each other. (00:06:30)
Brother From Another Series - S8-E16
Continuity mistake: In the shot where Homer yells, "Marge, I'm going to look for the kids," their door is shut. After Homer sees the wave and runs back inside, their door is open all of a sudden.
Continuity mistake: When the robbery happens, Homer steps on the robber's feet, and we can tell he has large shoes. When they show video of the robbery on the news, the robber has regular shoes. During the hearing, they watch the video again. His shoes are back to long again.
Homer's Triple Bypass - S4-E11
Continuity mistake: When Krusty bursts into the room, the shot ends with him having his arms and legs bent. In the next shot, he's straight as a ruler. (00:15:10)
Continuity mistake: When Homer says he's going to the cinema, we see his drinking bird working in front of the computer. It makes a key press on the lower right of the keyboard, however on the following close up shot of the bird pressing the Y key it is a standard qwerty keyboard layout.
Continuity mistake: When Sherri and Terri raise their hands and say "like us Mrs. Krabbapple" they raise their hands over their heads. Camera cuts and their hands are a lot lower. (00:04:20)
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: In Homer's flashback, when the pimp chases Homer, who is covered in garbage, Homer runs away from him on one side of the street. When Homer runs on the other side of the street, he is not covered with garbage. When he climbs a ladder and falls into a manhole, he is covered with garbage again.
Continuity mistake: When the teacher is looking out of the window, Bart has his paper in front of him on the desk. The paper disappears in the next shot, but reappears when Bart takes Martin's paper off the table and puts it on his desk. (00:06:10)
Tree House of Horror V - S6-E6
Continuity mistake: In "Nightmare Cafeteria", a teacher walks into the classroom and sees Bart sitting at his desk facing backwards. At this point, you can see the lockers behind the teacher are white, but in the next shot they are blue.
Tree House of Horror V - S6-E6
Continuity mistake: In "Nightmare Cafeteria", when Bart is being served his lunch at the lunchroom, his tray is initially plain but in the next shot it is now divided into six squared segments.
Tree House of Horror V - S6-E6
Continuity mistake: In "The Shinning", Homer is eating a bag of crisps while sitting on the sofa and you can see "Potato Crisps" logo on the bag is coloured red, but in the next shot it is now blue.
Continuity mistake: The comic book guy should be seen on the ground when Bart comes to the music store, but he has disappeared.
The Lastest Gun in the West - S13-E12
Continuity mistake: At the start of the episode, the dog eats Bart's clothes through the letterbox, but a minute later, when the dog next comes to the house and Homer opens the door, there is no letterbox.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: Dr. Hibbert's clothes keep changing during the song near the end. He goes from having his white lab coat, a blue sweater, then a pink sweater.
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