Revealing mistake: During the scene in which Lou forces himself on Kim in the lunchroom, donning a black ski mask, Kim's brother Alex jumps up to his sister's defense. Just before Alex throws his first punch, Kim screams "Michael," referring to the actor's real name Michael Tough. Kim then correctly screams "Alex," the name of the character he was playing in the film.
Revealing mistake: A close-up shot of Robin shows she's faintly breathing when she's supposedly dead.
Answer: Alex is not the typical one dimensional slasher serial killer, but rather a complex individual with conflicting motivations. The lipstick is a symbol that he is portraying the hurtful people from his past even as he kills them.