Missionary: Impossible - S11-E15
Continuity mistake: When Q'Toktok says "I told you we should have asked them", his hair is black instead of grey.
Pygmoelian - S11-E16
Continuity mistake: When Moe is reading the script there are no pink pages in the book, but when the director says "pink pages are dreams" they show pink pages that weren't there before.
Pygmoelian - S11-E16
Continuity mistake: When Moe is going to get a plastic surgery, the surgeon draws some marks on his face. You see Moe from a side view, and the marks on his face aren't visible from that angle. However, the marks on his face suddenly appear and you can now see them from that angle.
Pygmoelian - S11-E16
Continuity mistake: At the start of the episode, Homer wakes the family up and they get in the car in their night clothes. When they arrive at the destination, they are dressed.
Continuity mistake: During the concert at Nelson's club, when the amplifier makes a terrible sound and everyone covers their ears, you can see that old Carl (sitting with Lenny) is pictured white. I mean, yellow. (He's supposed to be black.)
Continuity mistake: When Lisa is on the television talking about her tax rise, we see inside Moe's tavern. Look at where Lenny and Carl are sitting because they have moved 3 or 4 seats down when we go back to them later on. And there is no reason why they would they move like that.
Continuity mistake: In the White House, Bart puts his cassette player front towards Lisa, but when Lisa pushes it out, it switches to face Bart between shots.
Continuity mistake: When the Ranger stops the Simpsons' car at the start of the episode, watch his "class ring". When he puts his hands inside the car it's on the left hand. However, the flies later eat his hand and take his ring, and it's suddenly his right hand they ate and took it from.
Other mistake: In the scene set in the future after Lisa, as the US President, held a conference with some journalists, just before the scene changes they show a black journalist with eyes not drawn among the crowd.
Continuity mistake: Just before Lisa's Presidential "refund adjustment" speech she pushes Bart's tape player off the desk and we can hear it smash off screen. Later in the episode when Lisa agrees to legalise it, he starts playing the same player.
Days of Wine and D'Oh'ses - S11-E18
Continuity mistake: When Moe tells Homer to sit on Barney's seat in front of the beer tap, Homer is sitting on a stool next to it. Homer suddenly switches seats between shots and the other seat disappears.
Days of Wine and D'Oh'ses - S11-E18
Continuity mistake: The police car door doesn't appear on Barney's arm until they watch the video.
Kill the Alligator and Run - S11-E19
Continuity mistake: When Homer beats the train they are on a road, but then another train comes by and hits them right where the road was.
Kill the Alligator and Run - S11-E19
Deliberate mistake: When Marge is sweet talking the sheriff, Bart unlocks all but Homer's foot chains, but when they're running for the gate, Marge, Bart, and Lisa's shackles can be seen.
Kill the Alligator and Run - S11-E19
Continuity mistake: When The Simpsons are being chased by the police, the cop is seen yelling at Homer. When the shot changes to Homer, the cop pulls out a gun from thin air and shoots.
Kill the Alligator and Run - S11-E19
Continuity mistake: The 2 guitarists in Kid Rock's band swap hair color when Kid Rock first arrives on stage.
Last Tap Dance in Springfield - S11-E20
Continuity mistake: Milhouse is barefoot when he and Bart discover the lion, but seconds later, when it chases them, he is wearing his shoes again.
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.
It's a Mad, Mad, Mad, Mad Marge - S11-E21
Continuity mistake: When Otto meets Becky at 'Der Crazy Kraut', there are a lot of children in the bus windows. However, just before he gives her the ring, the kids have now vanished.
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.
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