It's just less silly, than to think he constantly wipes his paint off, whenever he is not currently prowling the rooftops. There's was a specific moment, I can't remember what happened, I think it was when he learned the truth about his mother. In the first scene, he is in complete costume, face paint and all. Then he learns new information, and the next scene has him sitting in his hideout, sulking, with the face paint off. So he took his time to wipe his face perfectly clean, before he decided to just sit down, do nothing and sulk around?