I Don't Wanna Know Why the Caged Bird Sings - S19-E4
Factual error: During Dwight's attempted bank robbery, he gets hit with a couple of dye packs, then appears a few shots later totally clean. The dye packs banks use are notoriously difficult to wash off once they're triggered; even if Dwight did manage to clean himself up, there would still be remnants of dye on him.
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