Factual error: During the theme, the Simpsons' mailbox flag is on the wrong side of the mailbox. (Flags are always on a mailbox's right side, when viewed from The Front. The one at the Simpson home is on the left side of their mailbox). (00:01:45)
Factual error: After Bart's prank call with Moe, you can see Bart and Lisa laughing. However the telephone's wire does not connect to the receiver. (00:09:40)
Factual error: When Bart declares war on Nelson, Herman uses the declaration from the Franco-Prussian war and puts "Bart" in place of "Otto Von Bismarck". The thing is, Bismarck didn't declare the Franco-Prussian War, Napoleon III of France did. A small error, maybe, but something that a war buff like Herman should know.
Mr. Lisa Goes to Washington - S3-E2
Factual error: When the piano keys are shown when it is played at the end of the episode, it is shown having one black key each time. Real pianos start off with three black keys, then two, then three and so on.
Factual error: When Rod and Todd Flanders are roasting marshmallows in the car, Todd's marshmallow was the only one above the lighter, even though both of them have turned black. (00:17:40)
Factual error: When Bart is trying to escape from the girls at the start, Bart's door opens into the room. This would mean the hinges would be inside Bart's room and the girls couldn't have been able to remove them.
Kamp Krusty - S4-E1
Factual error: In the last scene, with the picture of the bus leaving Tijuana, it says "Leaving Tijuana" above the gate leading into the city.
Homer's Triple Bypass - S4-E11
Factual error: I get it, it's a comedy. But after open heart surgery, you are sedated for 1-2 days and on a ventilator. So, Homer even being awake after open heart surgery is completely false. Also, as someone who has had open heart surgery, you can barely move your chest because your sternum is fractured.
Factual error: When Selma throws Moleman out of her car, the passenger door is hinged at the rear instead of The Front as it should be on a relatively-modern hatchback, and the window crank is visible on the outside of the door.
Factual error: As Bart, Homer, Ned and Todd drift away from land in their boat, we see the clouds moving away. The clouds would not move that fast at the speed that the boat was going.
The Boy Who Knew Too Much - S5-E20
Factual error: Apu (an immigrant from India) could not have been selected for the jury because he is not an American citizen, and this was before he became a naturalized citizen in "Much Apu About Nothing".
Factual error: When you see Ned Flanders put the earth back inside the hole, he puts it back in much faster than is possible. In one shot, he is only just starting to put it back in, then you see Bart who talks to himself for a few seconds, then back to Flanders, who has finished burying what is later to be revealed as the plant that he (Ned) drowned.
Lisa on Ice - S6-E8
Factual error: The clock in a hockey game does not run during a penalty shot.
Factual error: The Suburb of Wooloomooloo where the chase starts is in Sydney, and the Simpson family are chased all the way to the American Embassy which is in Canberra, a distance of at least 150 kilometres. That's some impressive running, especially for Homer.
Who Shot Mr. Burns? (2) - S7-E1
Factual error: When Chief Wiggum opens the revolver's chamber, there's 5 rounds with one open slot. In the next shot, we see the reverse end of the chamber and it's drawn in such a way to indicate those 5 rounds all have bullets in them still, meaning the empty slot is from when Maggie shot Mr. Burns. But revolvers don't eject spent shells automatically and no one handled the gun after it dropped on the floor. So the empty casing should have still been in there when Wiggum opens it up for the first time.
Who Shot Mr. Burns? (2) - S7-E1
Factual error: Chief Wiggum visually compares a bullet taken from Homer's gun to the bullet removed from Burns and concludes that they are exactly the same. Excluding the obvious forensic violation, the bullet removed from Burns is still whole and within its casing, meaning that either Maggie took the time to remove the casing and delicately shove it in Mr Burns' bullet wound (which is dumb) or the gun fired the whole casing along with the bullet (which would have blown up the gun).
Tree House of Horror VI - S7-E6
Factual error: In "Nightmare On Evergreen Terrace", Martin has a dream, in which he speaks Latin. At one point, he says a verb that doesn't exist: "morire". The words is "mori" (to die), "moritur" (noun dies) or "moreris" (you die). The "moirie" is also on the blackboard behind Martin. (00:08:20)
Tree House of Horror VI - S7-E6
Factual error: During the "Attack of the 50 ft. Eye Sores" segment, the family steps into the footprint of the giant donut guy to look at the label. The label should appear to be spelled backwards, but it was not.
Factual error: If Homer's stomach was really caught on the towel rail the way they show it to be, he wouldn't be able to see the scales at all without having to look round it.
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