Continuity mistake: Kim is at the kitchen table with her brother Alex. Kim has a necklace on. Kim asks Alex about having a date for the prom and all that is around her neck is a gold chain. The shot then cuts to Alex and then back to Kim and now there is a gold star hanging from her necklace.
Continuity mistake: When Robin lays there after she dies her head's facing forward, a shot later her head's turned to her left.
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.