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 Bart and Lisa are looking at the globe, Bart points out Argentina and 'Ran McNally.' 1) Next time you see the globe, it is showing Africa and Asia 2) Asia is shown incorrectly and 3) The equator has disappeared.
Skinner's Sense of Snow - S12-E8
Factual error: Superintendents are the ones who decide whether or not schools should be closed for snow days, not school principals.
My Mother the Carjacker - S15-E2
Continuity mistake: When Homer is looking for a message to stop Grandma Simpson and the jail bus on the electric sign he has Bart with him. Then Bart is not on the bus with Homer and Grandma, but he is back at the end of the episode.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: The Springfield Isotopes win the championship at Springfield Stadium and it's daytime. But Homer and the guys watch the game live on TV at Moe's Tavern, and it is nighttime.
Deliberate mistake: When Bart is in the genius school, the teacher asks him if he knows what happens if he adds an acid to a base. He replies yes, adds them anyway and the lab explodes and a green goo comes out, turning Bart green. If you add an acid to a base, you just get salt and water.
Continuity mistake: At the end, you can briefly see Dr. Marvin Monroe. The cigar he is holding instantly changes from white to brown. (00:21:25)
Continuity mistake: The guardrail at the Springfield Gorge keeps changing between shots when Bart is about to make his big jump; in the first wide shot there is a short rail opposite the "stone ramp." Then in the Bart-POV shot from atop the ramp, the rail is much longer, and the parking lot and picnic area behind it have disappeared. And when Homer is actually jumping the gorge, the rail disappears altogether.
Bart Carny - S9-E12
Continuity mistake: When the Simpsons are cleaning their house, the painting above the chair goes from a picture of Maggie to a picture of a boat.
Continuity mistake: Abe's girlfriend dies in the middle of this episode, but at the end, seconds before the end credits, you can see her walk behind some other old people.
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: During the concert at Nelson's club, when the amplifier makes a terrible sound and everyone covers their ears, you can see that old Carl (sitting with Lenny) is pictured white. I mean, yellow. (He's supposed to be black.)
Continuity mistake: When Homer and Marge are on the plane, they both have seat belts on. However, when Marge gets up to run up and down the plane, both seat belts have disappeared.
Pygmoelian - S11-E16
Continuity mistake: When Moe is reading the script there are no pink pages in the book, but when the director says "pink pages are dreams" they show pink pages that weren't there before.
Continuity mistake: When they are riding the boat type raft, the stripes change from red on the left and black on the right, to the other way around and then back again.
Springfield Connection - S6-E23
Continuity mistake: When Homer first spots Snake dealing, you see Marge with a handbag. In the next shot, the handbag has disappeared.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: In every other episode, the bar at Moe's Tavern is a regular L-shape. In this episode, it has somehow gained two additional angles on the long side, making it a Z-shape (plus the angle to the short end, which is not shown).
$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)
Saddlesore Galactica - S11-E13
Continuity mistake: During the BTO concert, whenever the camera focuses on the crowd, the Simpson family is seen at The Front of the crowd. When the camera focuses on the stage, the Simpsons are at the very back of the crowd.
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.
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