Continuity mistake: In the video store, right after Homer picks up the tape, Maggie switches arms. (00:06:05)
Lisa's Pony - S3-E8
Continuity mistake: The people sitting behind Marge during the talent show keep changing/disappearing. (00:02:10 - 00:06:00)
Like Father, Like Klown - S3-E6
Continuity mistake: When Bart and Lisa see Reverend Lovejoy, their chairs keep moving closer/separating between shots. (00:13:05)
Continuity mistake: When all the salt spills out onto Milhouse's lunch, the salt that was on his food tray has disappeared. (00:10:50)
Continuity mistake: When Ralph and Bart are playing cards, Ralph has four cards in his hand. In a following shot he has five then back to four cards again.
Continuity mistake: In the scene where Homer is on stage in Springfield, he's wearing shorts. When he jumps off the stage after dodging the cannon ball, he's wearing pants.
I'm Goin' to Praiseland - S12-E19
Revealing mistake: In one of the scenes (I think it is when they first discover the alleged 'miracle') you can see people in the background walking out of the park. But they are not walking out of the park at all, they are walking into the wall.
Continuity mistake: In the last scene when Homer is about to attempt the loop trick, it is seen several times that the Mafia guys are not standing in a straight line. In all shots they are except the one where Homer fails, and then says "Ta da,". The Mafia are shown head to head in a straight line.
Continuity mistake: When Bart is trying to make the toilet water flow the other way, in one of the flushes the toilet begins to dispense water before Bart pulls the chain.
Continuity mistake: In the scene where Selma and Troy McLure get caught by the press outside the resturant, Selma and Troy swap places between shots.
Continuity mistake: At Moe's, when Homer takes hold of the telephone its color is red, but then changes to blue as he speaks to Marge. (00:02:30)
Continuity mistake: On the trip back from the gardens, Homer rear ends the car in front of him on the bridge which sends Maggie flying out of the car. In a long shot of the bridge whilst Maggie is in the air you can see the car has changed to an orange color instead of the usual light purple color. The two cars in front of them also change during shot. The one in front of the simpsons changes from a normal red mid sized car to a blue van, whilst the car in front of that one changes from being a green car to a blue one during the aerial shot of Maggie.
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: Right at the beginning of this episode, Homer is wearing a watch on his left hand, and he is still wearing it in one shot when he's in the car, but when he reclines his chair it is gone. (00:00:30)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The remote control for the robot in Bart's bedroom appears from nowhere. (00:08:30)
I, (Annoyed Grunt)-bot - S15-E9
Audio problem: After watching 'Robot Rumble', Bart tries to dissuade Homer from building a robot by listing his other "talents". The voice and Bart's mouth movements don't at all match. (00:06:20)
Homer's Barbershop Quartet - S5-E1
Audio problem: After Jasper has sung on the stage to Homer, Apu and Skinner, they simultaneously say "Next". But if you listen carefully you can't hear Homer's voice.
Burns' Heir - S5-E18
Continuity mistake: When Mr. Burns is sitting in front of the fireplace, he has his normal blue outfit when seen from behind, and a purple night gown when seen from The Front. (00:02:50)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Audio problem: When Kang and Kodos land in Springfield and hit Mayor Quimby with a club, one of them says something but his mouth is not moving.
Like Father, Like Klown - S3-E6
Continuity mistake: In Krusty's story after he has his makeup washed off by a rabbi, just after his father speaks to him his makeup suddenly reappears. (00:09:40)
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Deliberate mistake: In "Dial Z For Zombies", Homer is shooting zombies with the shotgun at the school. When he shoots the first two he just shoots them twice. Every other zombie he shoots requires him to slide the gun. It doesn't when he shoots the first couple of zombies. (00:19:50)
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