There's No Disgrace Like Home - S1-E4
Revealing mistake: When the Simpsons are eating at the dinner table, Marge's necklace keeps flashing white.
Revealing mistake: When Bart makes a copy of his photo for Lewis, footage of Milhouse inserting a coin into the copy machine is used. You can see Milhouse's pink shirt sleeve instead of Bart's orange shirt sleeve. This same shot is again reused a third time seconds later. (00:09:55)
Revealing mistake: The blonde woman's midriff (from the Space Mutants movie) flashes pink for a frame.
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.
Revealing mistake: When Fat Tony says,"I am not so much disappointed as I am blinded with rage", the dark circles under his eyes disappear for a split second.
Scenes From a Class Struggle in Springfield - S7-E14
Revealing mistake: When Lisa is first shown riding the horse, the horse's eye is colored solid red.
Revealing mistake: During Skinner's speech to the students in the school cafeteria, two Allison Taylors are seen sitting on different sides of the cafeteria.
Revealing mistake: When everyone is in Ned's shelter, the woman in the top left hand corner with brown hair and brown skin briefly has 2 pupils in each eye.
Brother From the Same Planet - S4-E14
Revealing mistake: The shot of Homer saying "Marge, when kids say bad these days, they mean good. And to shake your booty means to wiggle one's butt" is recycled from the opening scene from Life on the Fast Lane. Notice the animation is of a much lower standard than the rest of the episode.
Revealing mistake: When Homer points at the donut guy, his right shirt cuff is colored yellow. (00:12:50)
Revealing mistake: Krusty's nose flashes white for a split second during his song for the winner of the Little Miss Springfield pageant. (00:15:06)
Revealing mistake: In one angle when the Flanders are having dinner, Ned's eyeglasses have no temples.
Revealing mistake: When Marge is yelling at Homer at the dinner table after Lisa goes to her room, the outline of Marge's mouth over her neck when her lips are moving shows the neck line in her lips. (00:18:50)
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.
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