Continuity mistake: In the scene when Homer is signing up for the naval reserve, the administrator gives him a pencil to fill out his form, but when the camera moves to The Front of Homer it changed to a pen.
Continuity mistake: In the scene at the United Nations, the Russian placard is just a placard. In the next shot, the placard is attached with a rod to rotate it at the push of a button.
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