The "spy" Richard Castle pretends to be is named "Steven Caldwell". Richard Castle tells this to Hans Brauer. Mitch Pileggi (Hans Brauer) played the recurring role of Colonel Steven Caldwell in Stargate Atlantis.
Beckett mentions her past relationship with Detective Demming
The film Castle is watching at the beginning of the episode is "His Girl Friday" (1940) with Cary Grant and Rosalind Russell. The quote they choose to use "We've got something between us nothing can change" is probably intended to describe the relationship between Beckett and Castle.
Castle finds a pen with a secret recorded message that then self destructs at the end of the recording.