Apart from the usual formula of the show, the killer is revealed to viewers in the very beginning.
When Castle visits the set of "Heat Wave" in L.A., he and the film's director pass by a set of an airplane fuselage. This is the real Castle (2009) set on which Nathan Fillion and Stana Katic shot the scenes of Castle and Beckett flying to California and back to New York.
Kelvin was working on lightweight ammo for the military. While this is a real issue, the writers got it backwards. A light bullet is useless; think of getting hit with a miniature marshmallow at 800mph, at worst you would get light bruising. Bullets must be very dense. But the casing, the brass part that contains the propellent, is sort of dead weight. If you could reduce the weight and volume of the casing, a soldier could carry more ammunition.
Castle gifting a hotel robe when the murder is solved is a reference to Beverly Hills Cop (1984), in which Detective Foley gifts Detective Taggert a robe when that murder is solved.