Continuity mistake: When the doctor brings the "Hair in a Drum" product from under his desk, you can see in front of Homer there is a bottle of Dimoxinil and two gravity boots. When we see a close of the product in the next shot, the bottle and gravity boots on the desk have disappeared.
Continuity mistake: When the doctor places the items that come with the Dimoxinil on his desk, he places the scalp massager next to the pad. When Homer asks the doctor how much, we cut back to the doctor and the scalp massager is now on the pad.
Continuity mistake: When Homer gets mad when Carl calls him "Chrome Dome", there is a fish stick on his plate, but in the next shot, the fish stick has disappeared.
Continuity mistake: When Homer is speaking to Carl and Lenny at the coffee stand, there is initially nothing in Lenny's cup, but a few shots later his cup is now full without him filling it.
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 talking to the doctor about using his health insurance, Homer's hairline above his ear vanishes in a shot then reappears.
Continuity mistake: When Homer and Karl are selecting a suit, just after Karl says none of the suits are to his liking, Karl's tie changes from green to red.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Bart is unpacking his things from the box, if you look at the mantelpiece, we can see that there is a candle on the right hand side of it. But later on, there is a candle on the left hand side which wasn't previously there. (00:02:30 - 00:03:15)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: In Hungry are the Damned, when The Simpsons are on the spaceship and the aliens show them the food, there are 3 pots and two plates. Yet when the shot changes there are 4 pots and no plates. (00:10:25)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When the Simpsons are about to eat on the spaceship, in one shot just before they eat there are 3 candles on the table, and when they all sit down they're gone. (00:10:40)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Homer is preparing the barbecue, he is wearing an apron that says "Mafia staff apron". After he goes to pick up the lighter fluid, it reads "Maffia staff apron", and after he has lit the barbecue, it is back to saying "Mafia".
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: After the aliens have dropped off the Simpsons in their back yard, Marge is seen wearing her usual red pearls. Except in the final shot of the family. Then her pearls are white. This is not due to the alien light source altering the colors in the segment, because Marge's pearls have been a dark color through the whole episode, even inside the alien spaceship.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: In "Hungry Are The Damned", when the family are looking up at the UFO and Homer says that the burgers are getting cold, the burger he is eating has a bite out of it. In his close-up it is a whole burger.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When the Simpsons are eating for the second time the alien on the very left, which previously had spots on his cheek, now has no spots.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: In the Raven scene, you can see Homer's drool on his jacket, but in the next shot and following shots it's gone.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: The shot glass that Burns places on his desk disappears for several frames before reappearing. (00:05:45)
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: After the safety expedition has taken place, we see that when everyone is in Burns' office that by his main doors there are 4 buttons on the wall. Yet when a shot from further away is shown, they are not there.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Marge is standing outside the Kwik-E-Mart, she is holding some papers with a picture of Mary Bailey and the words "Re-Elect Bailey." But in a long shot of Marge in the next shot, the papers she is holding in her right arm are now completely blank.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr. Burns is drinking on his desk, a frame is misplaced. His shot glass, for a split-second, moves from its original position, to the edge of the table, and back.
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