Revealing mistake: In the shot of Skinner admiring his tater tots, he is interrupted and lifts up his tray. As he inspects he tilts his tray to at least a 90 degree angle but everything, including the milk, stays in exactly the same spots.
Bart Gets Hit By a Car - S2-E10
Revealing mistake: After Marge has been in court, Mr Burns' lawyer says "Thank you very much Mrs Simpson", and when he does it, the top of his head above his glasses is less pale than the rest of his face.
Homer vs. Lisa and the 8th Commandment - S2-E13
Revealing mistake: When Homer is imagining being locked in the jail cell and he turns around to find he is in his own home, he turns to look at his family. There is a close up shot of his terrified face, and the people in the background watching the game (I think it might be Lenny and Carl) have no eyes. The rest of their face is fine, but their eyes are missing.
The War of the Simpsons - S2-E20
Revealing mistake: When Ned says "Crème de cassis" while describing what was in the drink he made. There are several animation errors in this shot. His head is disconnected from his body, and his nose disappears. Also, a part of his face is missing between his fingers while he does the 'OK' hand gesture.
One Fish, Two Fish, Blowfish, Blue Fish - S2-E11
Revealing mistake: In the credits it shows Homer eating pork rinds. This is a reused scene from "Moaning Lisa."
Revealing mistake: While Homer is waiting for Marge to come downstairs, both Patty and Selma are wearing turtlenecks. When Homer thanks Mr. Bouvier, in the next wide shot as the twins nod their heads, both of their turtlenecks are not colored in properly at their torsos, so the background is visible through their bodies. (00:16:30)
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: 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 talking to the doctor about using his health insurance, Homer's hairline above his ear vanishes in a shot then reappears.
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