Tom Welling, who played Clark Kent for 10 years, sings "Dust in the Wind" by Kansas in this episode. On top of conveying Lt. Pierce's depression, the song is a subtle nod to Welling's iconic character, who is of course from Smallville, Kansas.
Lucifer says the episode title.
Charlotte drank three gimlets at lunch---the quintessential LA noir cocktail, enjoyed by Raymond Chandler's Philip Marlowe---made from gin and lime cordial, and named after the sharp, hole-punching carpenter's tool.
The titular "Pinhead" is the intended victim of the murder, so called by Lucifer after the antagonist (Pinhead) of the Hellraiser films, because she is seen at one point having facial acupuncture. Hellraiser was also the original, intended title of the John Constantine comics, changed to Hellblazer for copyright reasons. Constantine and Lucifer are well acquainted.