Revealing mistake: When Smithers makes Mr. Burns his Wine Spritzer, Burns makes Homer Employee of the Month. While Smithers is pouring the stuff in the bottle, his left hand turns black for three frames. (00:10:30)
Continuity mistake: When Homer and Barney are talking about the lottery, Barney says, "130 million." Then, they set their mugs on the table but when they all run off their mugs have disappeared. (00:01:50)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: In the parking lot, when Carl arrives, he is wearing a blue tuxedo. It changes to a lighter blue, and then back to its normal color when he gets in the car. (00:07:05)
Continuity mistake: When Burns first shows the team the nerve tonic, the "&" on the 'Brain & Nerve Tonic' label is facing backward, but as Burns pulls it away it faces forward. Then as he moves it around as he's talking, the "&" switches between facing forward and facing backward again. This happens all in the one shot.
Radio Bart - S3-E13
Continuity mistake: When Marge puts Maggie to bed, her pacifier changes from red to light brown between shots. (00:08:10)
Continuity mistake: As Martin reveals his Honor Rollor at the time trials, we can see Bart on the right side of the screen. He suddenly appears beside his car in the next shot. (00:13:00)
Lisa's Pony - S3-E8
Continuity mistake: Before Lisa licks the salt lick, there is another horse in the stable which disappears. (00:14:30)
Lisa's Pony - S3-E8
Continuity mistake: In the kitchen, there is a clock on the wall that changes time from 07:10 to 09:10. (00:12:10)
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When one of Marge's sisters says, "He blew all your savings on jack o'lanterns.", one of the armrests on the sofa is black for some reason.
Bart Carny - S9-E12
Continuity mistake: In the end of the episode when the family has reclaimed the house and are cleaning up the living room. As Homer mentions about letting the Cooders stay, Bart tells Marge to get him away from the window. She is standing right next to the couch in the lounge but the very next shot she lowers her hands and pats the couch yet is now in the family room. (Note: There was a few shots that showed there was two couches so the mistake is with Marge suddenly moving not the couch.).
Continuity mistake: When Edna waits in The Gilded Truffle, she checks her watch. In the next shot the watch has gone. (00:15:40)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: When Marge comes home after the bogeyman incident, Homer trips over a footrest. You can see Bart sitting there however his pyjama's are a dark green color when before they were a bright green color. (00:16:35)
Like Father, Like Klown - S3-E6
Continuity mistake: When Krusty rings his father, there are glasses on the bedside table. In the next shot they are gone. Meanwhile the other objects on the table have moved around.
Tree House of Horror VI - S7-E6
Continuity mistake: For most of "Homer3", Marge's shoes are red. When Frink explains that Homer is 3rd Dimension, Chief Wiggum says, "Slow down, egghead". During this shot, Marge's shoes are green. When Homer complains, Marge's shoes are back to red. (00:18:05)
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Genesis Tub,' when Skinner is grading the universe in the tub, his clipboard changes from brown to blue. (00:17:55)
Continuity mistake: As Nelson crosses the finish line at the time trials, The Front piece of wood on Bart's car breaks off. It is attached to the car again in the next shot. (00:14:10)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: At the very end of Part 1, Homer changes position between shots, and when Flanders wants a huge castle, it suddenly changes back to his normal house. (00:08:30)
The Trouble With Trillions - S9-E20
Continuity mistake: In the scene where Homer is eating a hot dog just before the post office closes for the day, the vendor behind the hot dog cart has a apron over his shirt. The very next shot the apron has disappeared. (00:05:05)
Continuity mistake: At the end of the episode, Homer puts twenty dollars into Moe's tips jar, but in the next shot the twenty-dollar note has disappeared. (00:20:40)
Realty Bites - S9-E9
Continuity mistake: When Marge finds out the Mr Hutz does real estate, the 'For Sale' sign changes from black to red and then back again.
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