There's No Disgrace Like Home - S1-E4
Audio problem: When Marge gets drunk at the picnic, she falls on Homer while saying "Homie, did you try the punch?", her lips don't move. (00:06:20)
Audio problem: When McBain is explaining about his movie on TV, we see a clip from his movie, in which he uses a machine gun. He throws it on the floor but we don't hear a sound of it crashing on the floor.
Audio problem: During Selma and Bob's conversation at the dinner table in the Simpsons' house, Bob says "Although kissing you would be like kissing a divine ashtray." His lips don't move when he says "although".
Audio problem: Ms. Krabappel is telling Bart about the laundry list of sicknesses he had to get out of the test. You can see her mouth doesn't match up when she mentions "...and that unfortunate case of rabies." The studio actually changed what Ms. Krabappel originally said which was "and that unfortunate case of "Tourette's Syndrome." [Some reports say that the original line of Tourette's Syndrome was left in syndications in certain areas. On the DVD version the rabies line has been used]. (00:16:00)
Audio problem: When Bart is attempting to skate over Homer's car with his friends watching, Milhouse says 'You're crazy Bart.' but his mouth never moves. (00:10:55)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Audio problem: When Homer is putting Christmas lights around the outside of the house, he falls from the roof. You can then hear Lisa and Bart sarcastically clap. But you can see they both have their hands by their side, and no-one is clapping. (00:04:55)
Scuse Me While I Miss the Sky - S14-E16
Audio problem: In Declan Desmond's film of Springfield Elementary shown at the end, Kearney and Dolph start beating Jimbo up. After Kearney says "Sellout," he says "Yuppie" in Dolph's voice. Then Dolph says "Soccer Mom" but in Kearney's voice.
Skinner's Sense of Snow - S12-E8
Audio problem: When Principal Skinner is watching the kids throw the books in the fire, someone goes to throw Huckleberry Finn into the fire. He says "Not Huck Finn. I spent hours crossing out the sass-back." While he says this, his lips don't sync with the words.
One Fish, Two Fish, Blowfish, Blue Fish - S2-E11
Audio problem: In this episode Homer makes a tape for Maggie because he believes that he is going to die. However the speech is terribly out of sync with Homer's mouth movements.
Audio problem: When the family are about to enter the Knowledgeium Homer says 'Will there be beer?' but his lips don't move.
Audio problem: When Homer and Marge are driving to the hospital, Marge says "Let's just say that Bart did it". But her mouth says something else when she says "Bart".
Children of a Lesser Clod - S12-E20
Audio problem: When the moon says, "You go, Homer,'" the words dont match what the moon says.
Audio problem: When Homer is in the asylum talking in his sleep, his mouth stays open when he's talking.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Bart gets the beavers to knock down the tree so that Clara can walk across, she gets onto it and starts walking gently. But when she walks gently, it sounds like she's walking quickly across the trunk.
Audio problem: In the beginning, we are at the power plant. We find out that Burns has packed his own lunch, and one thing he packed is a bullion cube. His mouth doesn't move right when he says "Bullion cube".
Audio problem: When Bart's dog is chewing on the TV remote, one of the shots on it is of "I Can't Believe They Invented It." with Troy McClure as the host. This is exactly the same shot from "Homer vs Lisa and the 8th Commandment". You can tell because Troy's voice is different. The lip sync is also out, revealing that the line "As an actor, my eyeballs need to look their whitest" is dubbed in.
Weekend at Burnsie's - S13-E16
Audio problem: There is an elaborate bass line right at the end of Phish's song; however, the bassist's fingers don't even move. There's no way he could play that line without moving his hand. (00:13:50)
It's a Mad, Mad, Mad, Mad Marge - S11-E21
Audio problem: When Becky is walking towards Otto in the wedding, there is a band playing music. You can hear singing but the singer's mouth isn't even moving.
Audio problem: Just after Homer has been knocked down by the cannon with the "No Litter" message on his stomach, you hear cheering but the crowd don't do anything.
Audio problem: At the end, where Homer is carrying Mark Hamill out of the theater and Mark says, "Shoot, I forgot my Light saber", his mouth doesn't match what he says, and it keeps moving when he's quiet.
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