The movie features the song "Good-bye Horses," by Q. Lazzarus. The song was also featured in The Silence of the Lambs (1991), another movie about a serial killer who skinned people and had issues with his mother.
Upon meeting Frank at the restaurant, Lucie says she's happy that he's not "Fat, with long black hair and greasy skin full of acne" which, whilst not flattering, would be an apt description of Joe Spinell's Frank, in the original.
As opposed to Frank initially coming across Anna at the park from afar as she's taking pictures of various people in the original film, Maniac (1980), in this film, she eventually comes across him at his mannequin shop when she's caught taking pictures of his mannequins through the display glass.
The trivia items below may give away important plot points.
Right after the scene when Frank kills the girl in a parking lot and he stands up with a knife in one hand and scalp in the other, you can see his reflection for a few seconds that is intentionally styled as the poster of the original movie Maniac (1980).
The film that Frank and Anna see at the movie theatre is The Cabinet of Dr. Caligari (1920). As they leave the theatre afterwards, Anna comments that she thought that the heroine was going to get killed at the end of the film to which Frank replies that the heroine was going to survive. She responds that the heroines would normally end up in mental institutions at the end of similar-type of films. In response, he states that at least the film has a happy ending. Ironically, surprisingly, and unfortunately, Anna herself, who is this film's heroine, does in fact get killed at the end of the film. Whereas, interestingly enough, in the original film, Maniac (1980), she survives.