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.
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).
When Lucie puts on music at her apartment the record is playing the 7" version of Q. Lazzarus's song "Goodbye Horses" while the actual record is clearly a 12".
When Lucie meets Frank at the restaurant, her underarms seem freshly waxed. Later in her apartment, there is visible gray stipple under her arms. This is likely a continuity error because hair does not grow that fast and the scene in question takes place immediately after the restaurant.