Audio problem: When Marge says she wants the padding that goes under rugs her lip movements don't match what she's saying. (00:13:25)
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)
Homer vs. Lisa and the 8th Commandment - S2-E13
Revealing mistake: When Homer is imagining being locked in the jail cell and he turns around to find he is in his own home, he turns to look at his family. There is a close up shot of his terrified face, and the people in the background watching the game (I think it might be Lenny and Carl) have no eyes. The rest of their face is fine, but their eyes are missing.
Tree House of Horror X - S11-E4
Continuity mistake: In the 'I know what you did-diddly-did' story, the Simpsons car keeps changing from dark purple to the normal pink colour.
Continuity mistake: When Marge goes in front of her painting after it is uncovered she stops with her head in front of Mr. Burns' genital area. In the next shot, her head is shown in front of Mr. Burns' hand.
Continuity mistake: When Homer is making a note for Marge, he scribbles out Patty's name and writes his own. When he writes it, the "signature" is neat, but when Marge reads it, it's sloppy. (00:14:30)
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Homer crashes through the security barrier then skids to a halt on concrete. But, a shot later, the car is on a field which wasn't there before.
Continuity mistake: When Marge and Homer are at the Springfield formal ball at the Country Club, about half way through the ball, there is a woman with her back to the camera as she is talking to Marge and Homer. Homer is on Marge's left side. In the next shot when Marge's back is to the camera and you can see Marge still talking to the woman, Homer is no longer on Marge's left side, he is gone.
Some Enchanted Evening - S1-E13
Continuity mistake: Bart is shown sitting tied up on the couch and Ms. Botz walks in carrying a tied-up Lisa in her arms before dumping her on the sofa alongside Bart. You can see that the rope Ms. Botz has used to bind Lisa is wound right around her body from the neck right down to her ankles. A few shots later when Maggie comes down and frees her, the rope tying Lisa's legs together at the knees has disappeared.
The Bart Wants What It Wants - S13-E11
Continuity mistake: When Bart is in the ice cream parlor breaking up with Greta, the waiter tells him "We get that a lot around here" and point over to Chief Wiggum and Lou sitting behind and to the left of Bart. Bart turns his head all the way to the side to see them. The focus then goes to Chief Wiggum and Lou, but when their part is done and the "camera" goes back to Bart and Greta, the policemen are sitting behind and to the right of Greta, so that Bart would not have had to turn his head to see them.
Continuity mistake: During the Itchy and Scratchy episode at the beginning, Itchy's hammer changes from being held above him to beside him between shots.
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.
Continuity mistake: When Homer is gambling with the gangsters, you can just barely see the shoulder of an ORANGE shirt that Bart is wearing, but in all other shots he is wearing his tuxedo. (00:12:10)
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When Bart and Lisa are at Sunday school, the teacher writes "HELL" on the board, which changes from being red to black between shots.
'Tis the Fifteenth Season - S15-E7
Continuity mistake: After Homer decides that he doesn't want to sleep with Marge, he goes downstairs and watches TV. He moves to a different side of the sofa between shots.
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".
Continuity mistake: When Marge is talking to Lisa in her room about Band Practice, Lisa is reading comics, eating potato chips, and there is a drink by her as well. The drink container starts out green with a light purple label, then goes to being grey with a red label then as Marge tells her story, the colours of the drink change again twice. (00:10:00 - 00:10:55)
Continuity mistake: Two guards take down and eat the embassy flag. But when the Simpsons look down at the frogs at the embassy, the flag is still up on the pole.
Revealing mistake: When Lisa is explaining to the curator of the museum why she didn't tell the crowd of what she learned about Jebediah Springfield, if you look in the background none of the people on the far sidewalk are moving, almost frozen in place with some of them with their arms in the air yet everyone and everything in the parade keeps moving right along.
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)
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