Continuity mistake: When the first photo is taken of Selma and Troy on their first date, Selma is wearing lipstick. When the photo is published, the photo shows her without lipstick.
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.
Other mistake: During the Planet of the Apes musical final number, as the chorus line dances on stage from left to center with the Statue of Liberty in the background; however, parts of the Statue (the pink background between arm and book) cut off the dancer's head as if it is in the foreground. (00:12:19)
Continuity mistake: During the Planet of the Apes musical segment, just before Troy McClure sings "Can I play the piano anymore?", he and Dr. Zaius are standing far apart. In the next shot, they are close together.
Continuity mistake: In the overhead shot of Patty smoking, she is sitting on a greenish-gold car, the car then turns blue in the next shot.
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