Other mistake: When Homer is being interviewed while feeding baby Lisa, there's a picture of 8 year old Lisa in the background.
Continuity mistake: When Marge enters "Your home from space" the address is still http://www.google.com, then the shot changes to Marge outside and then shows the computer again where the address is now http://yourhomefromspace.com.
Stop Or My Dog Will Shoot - S18-E20
Continuity mistake: In the scene where the dog chases Snake into a playground, Santa's little helper starts pulling the ropes off the top of the climbing frame, in one shot the dog has two ropes left but when we see Snake the dog chews through one rope and the whole thing falls.
Factual error: In the episode with Donny, when Bart sees principle Skinner go into the school to meet with the rat, the door is backwards. The bars that are pushed in to open a door are always on the inside.
Character mistake: Before their first performance, the director of "La Boheme" wishes Homer good luck. To anyone in professional theatre, doing so is the cardinal sin of theatrical superstition and is never done; the appropriate phrase is "break a leg."
Character mistake: When Mr. Burns and Smithers are walking through the morgue, the sign on the wall is incorrectly spelled "Hospitial Morgue."
Continuity mistake: When Homer has his car towed from the bank, it is hooked up at the rear. When they arrive at the impound lot, it is hooked up at The Front.
I Don't Wanna Know Why the Caged Bird Sings - S19-E4
Factual error: During Dwight's attempted bank robbery, he gets hit with a couple of dye packs, then appears a few shots later totally clean. The dye packs banks use are notoriously difficult to wash off once they're triggered; even if Dwight did manage to clean himself up, there would still be remnants of dye on him.
Treehouse of Horror XVIII - S19-E5
Continuity mistake: When Marge puts the logo Hugh Laurie in the microwave, he splatters in the corner. Next shot the splatter is in the middle of the microwave. (00:01:00)
Treehouse of Horror XVIII - S19-E5
Factual error: In the Mr. And Mrs. Simpson segment Homer is firing a minigun at Marge and three of the barrels are seen spitting fire. A minigun however only uses one barrel at a time to fire.
Treehouse of Horror XVIII - S19-E5
Continuity mistake: When Marge shoots Chief Wiggum, the arrow goes through his tie. When they roll on top of him, the arrow isn't through the tie anymore.
Continuity mistake: As Bart is about to enter his house after trying to impress his friends by krumping, you can see he is entering The Front door. However, in the next shot when he gets inside and Marge is waiting you can see that he has entered the family room, which is only accessible through the back door. Entering by The Front door would place him by the stairs, at The Front of the house.
Continuity mistake: When the school bus drops off Bart and Milhouse at the Simpson house, Bart puts his backpack on frontwards and starts krumping. When he walks through The Front door, he is still wearing his backpack on his front. It then cuts to inside the house, and we still see him coming through the door, but the backpack is gone.
Continuity mistake: When the men from Festival Cruise Lines arrive at the Simpson house, they park in the left-hand lane (closest to the house) with the car facing oncoming traffic, seen both when they first pull up and, more, in the background while informing Milhouse about his parents. But in the overhead shot of the house, the car is parked the other way around, following the direction of traffic.
Factual error: The cover of "World's Finest Comics" #94 is shown on the wall at the comic book store. It features Superman with a sign that says, "Gotham or Bust," and Batman gulping. The actual cover of "World's Finest Comics" #94 shows Superman being sprayed with liquid kryptonite while Batman and Robin catch sight of him.
Continuity mistake: In the surgeon's office there are three certificates on the wall with ribbons on them. In the first shot there are two red ribbons and a blue one but in the shot where Homer stands up to read the bill all the ribbons are red.
Continuity mistake: When Bart says "Stop feeling sorry for him", Dr. Robert Terwilliger Sr. is seen sitting in the audience, even though he is supposed to be sitting in the witness stand.
Eternal Moonshine of the Simpson Mind - S19-E9
Continuity mistake: Near the end, when Homer says "I'm a genius", Krusty is seen with yellow skin, but is later seen with his usual white skin.
Continuity mistake: When Marge is watching Homer's "Margarine" music video, the coffee in her cup keeps changing.
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