When Castle and Beckett call Esposito at the precinct and he puts them on speaker phone, you can hear them listing reasons over the phone. Beckett says the same reason twice in a row, once right as Ryan walks up, and the other while he is standing there listening.
Billy Squier's "The Stroke" is used for the "Beckett's revealing outfits" montage. However, the song is actually about the music business, not about sex, and "Castle" is hardly the first show to make this mistake.