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)
Who Shot Mr. Burns? (1) - S6-E25
Revealing mistake: Right at the beginning, watch as Principle Skinner enters the classroom, there's a clock on the top left hand of the screen. The majority of the left side of the clock is not drawn in.
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.
Other mistake: When somebody throws a cola can at Homer, the can never hits the ground.
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.
The Day the Earth Stood Cool - S24-E7
Audio problem: When Homer says "Can I man hug you?", he mouths "Can I brother hug you?"
Little Girl in the Big Ten - S13-E20
Revealing mistake: When Bart says "I don't feel so good" after being bitten by a mosquito, his lower body under the table is not visible.
Hunka Hunka Burns in Love - S13-E4
Audio problem: When Marge says "New underpants?", she is mouthing "New boxers?"
Audio problem: When Lisa says "Oh no, somebody took my bike", she is mouthing something else.
Revealing mistake: There are two Ruth Powers in the same shot, when the people are crowding on Homer at the mall.
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.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: During Homer's flashback, Homer passes the sign that says "Jeremiah's Johnson" twice.
Brother From Another Series - S8-E16
Continuity mistake: Ruth Powers' hair is red in one of the shots of the protesters. Her hair is brown in other shots of her.
Continuity mistake: In the shot before Nelson says "Hey, Simpson. Race you", Ralph is seen sitting on the row in front of Martin. But when Ralph says "Go, banana" he is suddenly sitting two rows in front of Martin. (00:05:25)
Character mistake: When Maggie starts speaking Ogdenvillian, Marge says that it is her first word. But in the episode "Gump Roast", everyone, the Simpsons included, all watched a video of Maggie saying her first word. (00:17:35)
Other mistake: When Bart is looking at Doctor Hibbert on the rowing machine, all the pictures on the walls behind him don't have faces on them.
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