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.
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.
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.
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