Continuity mistake: When watching the draw, the family have their TV dinners on their lap, which seem to instantly disappear between shots. (00:05:10)
Continuity mistake: When Homer is covered in gold and goes into Burns' office, Burns has 2 folders on his desk. One yellow and one white. However, the white folder becomes yellow in one shot. (00:04:50)
Continuity mistake: Homer asks Bart and Lisa what they will do with their money, Bart has a can of Buzz cola in his hand and when Lisa speaks the can simply vanishes from Barts hand. (00:04:20)
Revealing mistake: When Homer is putting up all the lost dog posters on the building that gets blown up, the stapler isn't on the poster. (00:17:30)
Continuity mistake: When Bart is pacing waiting for Sant's Little Helper, the time on the clock changes drastically when the nurse opens the door. (00:11:40)
Continuity mistake: When Homer suggests the family becomes a group of acrobats, a clipboard suddenly appears on the table in front of Marge. (00:11:30)
Continuity mistake: When Marge is listing all the cut backs, the calculator on the table keeps appearing and disappearing between shots. (00:10:30)
Continuity mistake: When Homer tells Marge to go and get all her money, he is holding her shoulder next to her necklace. Camera changes and his hand is lower.
Continuity mistake: The colour of the sign Moe switches on at the start changes from yellow to red. (00:01:50)
Other mistake: In the scene set in the future after Lisa, as the US President, held a conference with some journalists, just before the scene changes they show a black journalist with eyes not drawn among the crowd.
Continuity mistake: When Krusty appears on stage he has a microphone that vanishes from his hands when he claps at the end of the song. (00:13:10)
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Continuity mistake: When Bart gets the Krusty doll, he pulls the pull string from the back of the doll. When the doll has finished talking, the pull ring has disappeared. (00:04:05)
Continuity mistake: When Millhouse first spots the spookhouse, there is a red item on the floor by him, as he walks towards the spookhouse the item has gone. (00:03:00)
Continuity mistake: When Homer comes into the kitchen to ask what 1 thing Lisa would want most, the milk carton and glass disappears from the table for a few shots. (00:07:10)
Continuity mistake: Homer says he wasn't sure if he was doing the right thing in regards to giving up doing to church. When he does he puts his fork down across his knife. When the camera cuts the two utensils are no longer crossed. (00:10:40)
Marge vs. the Monorail - S4-E12
Continuity mistake: When the sticker reveals the 1964 world fair sticker on the monorail, the world fair sticker is blue. Shot changes to a high angle shot and now the sticker is white. (00:16:40)
Marge vs. the Monorail - S4-E12
Continuity mistake: Cobb's hair in North Haverbrook changes length between shots. (00:14:10)
Continuity mistake: When Lisa says she will do the pageant, her clock goes from 8:05 to 7:55. (00:08:30)
Revealing mistake: In the opening sequence's parody of the series where Bart becomes fat and comes out from school on his skateboard, he theoretically should go down the stairs, instead his silhouette suddenly climbs up on the wall next to him, revealing a mistake in the post-production's animation. (00:06:05)
The Mook, the Chef, the Wife, and Her Homer - S18-E1
Revealing mistake: When Fat Tony says "The Calabresis. My archenemies in waste management." while driving the carpool, a huge line briefly appears around his cheek and mouth.
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