Continuity mistake: The way the chapstick is held out for Bob in prison changes from one shot to the next. (00:04:40)
Continuity mistake: When Bob is telling his story about picking up rubbish on the side of the road, we see Bob in The Front of a line of people. When we see the convicts in the reflection of the trooper's sunglasses there is someone in front of him. (00:03:20)
Continuity mistake: During the meal at the start, the food on Bart's plate changes between shots. (00:02:50)
Continuity mistake: At the dinner table, we see an overhead shot of the table and there is a glass of milk next to Homers hand. As the shot changes, this glass is now gone from that location and moved to nearer Bart. (00:02:50)
Continuity mistake: When Lurleen is in the studio with the Simpson family, Homer has his arms crossed. When Bart asks to do a solo his hands are now in his pockets. (00:14:50)
Continuity mistake: When Marge and Homer are arguing over his boyhood dream, the time on clock jumps forward between shots. (00:13:20)
Continuity mistake: As people throw stuff at the redneck bar, the guy who introduces Lurleen is leaning to his left then instantly to his right between instant cuts. (00:06:10)
Revealing mistake: When the bartender points to the Fudd neon sign behind him, his hand goes through the sign. (00:05:40)
Continuity mistake: When Santa's Little Helper is eating from his bowl after his operation, the amount of food in his bowl increases drastically. (00:12:50)
Continuity mistake: When Bart is in the car and asks when the dog is going to get his operation, his hand is not on Lisa's seat. When the shot changes, to show the whole car, it is. (00:07:50)
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: 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)
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