Continuity mistake: After Phil eats the "horse" egg at Moe's he asks to be taken to the hospital, and when it cuts back to Homer at the power plant, the direction of the stripes on Homer's tie switch to the opposite direction, mid shot. The same thing occurs again later. First, when Homer is standing outside the office while Fred talks to Burns about the benefits package, and also when Homer can't stay for Marge's turkey breakfast. (00:07:05 - 00:12:20)
Continuity mistake: While Homer, Carl, and Lenny are at Moe's with their new bud Fred, in the interior shots the swinging front door to Moe's swings open on the left side, but in the exterior shot when they all leave Moe's, that door still swings open on the left side, opposite to the interior shots. (00:08:00)
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