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)
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Audio problem: In "Clown Without Pity" when Homer yells "The doll is trying to kill me, and the toaster's been laughing at me!" his mouth doesn't move. (00:06:45)
Continuity mistake: When Chief Wiggum pulls Homer over for speeding, all the clown decorations on his car have disappeared.
Revealing mistake: In one angle when the Flanders are having dinner, Ned's eyeglasses have no temples.
Continuity mistake: When Ned is saying grace, the plates on the table contain no food, but when Homer comes through the window there's food on the plates.
Krusty Gets Kancelled - S4-E22
Continuity mistake: When Bart and Lisa are helping Bette Midler pick up trash on the highway, Bette picks up an empty can which says Buzz Cola on it. Just as she yells, "You pigs!" the label on the can switches to Duff Beer.
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)
Continuity mistake: At the end when Nelson's goons are holding on to Nelson, they both have brown skin. But in the next shot, one of them goes back to having yellow skin.
Continuity mistake: When Homer is rolling around on the grass outside the house with Bart, Lisa, Santa's Little Helper and Snowball II after the hair formula works, Snowball II is drastically larger than usual in the overhead shot.
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)
Continuity mistake: During the wedding, look at the man with the blue hair carrying the tray with hors d' oeuvres that Homer is eating. When Homer says "Hey wiener boy. Where do you think you're going?" the man's collar changes from white to black instantly.
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.
Audio problem: At the gorge, Nelson says, "Where is he? I thought he said noon!" But Milhouse's mouth is also accidentally lip synced to Nelson's dialogue.
Continuity mistake: A huge fight begins in front of Mark Hamill's stage. Homer, Quimby, Hamill, Bart and Lisa escape the fight through an emergency exit right behind the people fighting. But in a shot of the five running out, the people fighting inside have disappeared.
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