Grandpa vs. Sexual Inadequacy - S6-E10
Other mistake: Look closely when the clerk scans the books. Ueberroth is a brown book, and Al Gore's book is green. The book that sends the message to Al Gore is the Ueberroth book.
Other mistake: While Homer is in Lisa's bedroom trying to make things right with her, there are three pictures taped to Lisa's mirror. After Homer tells her the music may help, in the next shot Homer walks over to stand behind Lisa. Those pictures taped to Lisa's mirror are weirdly behind Homer's reflection, as if the pictures are taped to the wall behind Homer. Three shots later, when Homer tells Lisa he can fix the dollhouse, his reflection is accurate in relation to those three pictures taped to the mirror. (00:19:20)
Other mistake: When Homer and Chief Wiggum fall into the waste, in the second shot, the cliff edge looks very weird. It seems to be transparent with Ruth's car floating in mid-air, and there is a big curved wall that doesn't have ground at the top.
Other mistake: There are two mistakes when Bart calls the Krusty Hotline: 1, The cereal box says the phone number is '1-909-O-U-KLOWN.' Bart presses eight buttons on the phone. 2, as he is dialing, you can HEAR seven buttons being pressed. (00:01:45)
There's No Disgrace Like Home - S1-E4
Other mistake: When Homer is at Moe's, there is a boxing match happening on TV. There is a bald guy who is getting considerably battered by the opponent and gets knocked out, and then for some absurd reason he is victoriously standing and smiling as if he had won.
Homer's Triple Bypass - S4-E11
Other mistake: In the beginning of the episode when Chief Wiggum orders a battering ram through The Front door of a house, Reverend Lovejoy opens the door and questions what they are doing. Chief Wiggum says "isn't this 742 Evergreen Terrace?" to which Lovejoy replies that it's the house next door. In the next shot, you see Snake pulling out of the garage and speeding away. Everybody knows that 742 Evergreen Terrace is, in fact, the Simpson residence. (00:02:40)
It's a Mad, Mad, Mad, Mad Marge - S11-E21
Other mistake: When the kids are holding the video cameras, there is no strap to keep their hands on the camera, so it looks like their hands are glued to the side.
Other mistake: When the Simpsons' drives the electaurus off the edge of the harbour, it is shown that The Front of the car goes downwards. When it cuts to the interior view with the Simpsons' screaming, the view from the back window is tilting down, suggesting the rear is going down and The Front coming up. But in the next shot the car is seen in the water with The Front down.
Other mistake: In the scene where the Simpsons are viewing the path of the Corvair's Re-entry, the blip representing the spaceship crosses the entire US from North-West to South-East in about three seconds. This is really impossible, even for something going as fast as a spaceship on re-entry would be.
Other mistake: In the shot before Marge says she will marry Homer, the right side of the screen is cut off a little. (00:08:25)
Mr. Lisa Goes to Washington - S3-E2
Other mistake: The first time we see all three children staring at the TV, the interior of the Simpson house seems different. (00:02:30)
Other mistake: Apu already knew Homer because in the flashback episode, Homer's Barbershop Quartet, they were in a band. However, in the scene where Homer enters the Quick-E-Mart, Apu refers to Homer as steady customer as if he didn't know him.
Other mistake: After the boxing match, the boys start "boo-ing" to the TV, and for a few frames Lewis goes from black to yellow, then to black, causing a flashing effect. (00:02:45)
Other mistake: When Marge sees the letter from Homer, she says "You won't see me again until I'm a man." On the paper though, it reads 'But you will not see me-' and the sentence is cut off, and the rest of the paper is blank. (00:16:10)
Scuse Me While I Miss the Sky - S14-E16
Other mistake: Bart and Lisa overload the nuclear power plant to create a city-wide blackout so everyone can see the meteor shower. All the lights in Springfield blow out. Yet when we see the Simpsons sitting on their lawn watching the shower, every single window in their house is yellow, as if every room has their lights on. It is the only house shown with power.
Tree House of Horror VIII - S9-E4
Other mistake: In 'Homega man', Homer goes into the bomb shelter and does not shut the door, and you can still see it open for a while after he is in there. Herman does not close it behind him - you can tell by his skeleton's position. But Homer opens the door to leave the shelter after he has eaten the food, and it must have been closed for him to have survived the atomic attack, because it vaporised Herman, who was only a few feet away.
Other mistake: After Ugolin (one of the French men looking after Bart) has taken Bart to the Chateau Maison, Cesar and Ugolin speak. (they aren't visible in this shot) Ugolin says "Escape is impossible", but the subtitles say that Cesar says it and vice versa for when Cesar actually speaks.
Tree House of Horror X - S11-E4
Other mistake: In "Desperately Xeeking Xena", at one point she approaches the Collector, who is about to get a light saber. We can see the back of the pouch that Xena is in, but the tape on the other side isn't visible, even though it is a transparent pouch.
Tree House of Horror V - S6-E6
Other mistake: At the speed that Homer was chasing the family outside the lodge at the end of "The Shinning", he would have caught them up with ease.
Other mistake: When Homer is giving people tartar sauce at the cafeteria, he says "plenty for everybody" with his mouth closed at the end of him saying it. However the photo in the newspaper is shown with his mouth open. Also, for the last part of "everybody" his mouth doesn't move.
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