Revealing mistake: When Barney says "How long will the story take?" after Bart offers to tell the mob his story, the upper half of Barney's face starting from his nose is a darker shade of yellow than his lower half. His shirt also changes colour. (00:01:40)
Revealing mistake: In the beginning, when the angry mob is chasing after Homer and Bart, there are two Dr Marvin Monroes. One of them is behind Mrs Krabappel and the other is next to Grampa Simpson. (00:01:40)
Revealing mistake: While Patty tells Selma "Look who's talking" after Homer debuts his new haircut, both of their chests up to their necklaces are the same color as their dresses. Selma's dress also suddenly has sleeves on it.
Revealing mistake: When the man with the white helmet and flashlight asks Homer if he's holding on to the can in the vending machine, a large scratch appears near the upper right corner of the screen over the man's helmet.
Burns Verkaufen der Kraftwerk - S3-E11
Revealing mistake: When Homer takes out the dollar bill from his back pocket right before he puts it into the vending machine, the left side of the screen is cut off a little. You can tell especially with how the trash bin in the bottom left has a splotchy white line next to it. (00:02:20)
Revealing mistake: When talking to the doctor about using his health insurance, Homer's hairline above his ear vanishes in a shot then reappears.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: When Homer brings Santa's Little Helper home, a single frame of Maggie falling off Marge's lap is misplaced.
Revealing mistake: When Homer says "Oh, baby we got him now" whilst arriving in the airport, you can see half of Doctor Hibbert's face in the background, but you can see he doesn't have any eyebrows or eyes.
Revealing mistake: At the U.N. meeting, Bart places his glasses down on the table to read out the Libyan exports. As he puts the glasses down, you can see they are unrealistically floating in the air.
Mypods and Boomsticks - S20-E7
Revealing mistake: When Bashir leaves the Simpson house, he doesn't have any eyebrows. (00:12:40)
Brother Can You Spare Two Dimes? - S3-E24
Revealing mistake: When Herb reads the article about Homer winning the $2,000 the writing on the newspaper (except the headline) is just gibberish. (00:09:20)
Revealing mistake: At the craft store when Homer and Bart go in, the door opens before Homer pulls the handle. (00:14:00)
Itchy and Scratchy: The Movie - S4-E6
Revealing mistake: When Nelson blinks right before Milhouse says "No one who saw the movie would say that", Nelson's right eyelid is white for some reason. (00:18:20)
Revealing mistake: When Nelson is offering Lisa the fraction quiz answers, right before Lisa says she's never cheated before and won't again, her right hand disappears for a single frame.
Marge vs. the Monorail - S4-E12
Revealing mistake: When Homer is driving along and singing, he passes three houses in the background. Those exact same houses reappear three times in the same shot even though he never turned around. (00:01:15)
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.
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.
Revealing mistake: There are two Ruth Powers in the same shot, when the people are crowding on Homer at the mall.
Don't Fear The Roofer - S16-E16
Revealing mistake: When Homer sits on Lenny's cake in Moe's bar, some of the frosting appears to stay in mid air, and when the frosting is on the wall, it doesn't slide to the ground like frosting would.
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