When Castle tells Beckett about the invitation to go drinking with the Indestructibles, at one point she cups his face. When the shot cuts, her hand is gone and she instead has her arms around his neck.
When Castle and Beckett listen to the recording of Lance's that Castle retrieved from Boothe's office, and Castle notices Beckett is listening with a set of headphones, the position of her hands on the earpads changes back and forth between shots.
While cleaning out Kate's kitchen she insists on bringing one of her own pots, says its an old favorite with memories, unfortunately the props dept left the sticker on it, so not an old pot at all.
It is claimed that Enrique Gomez was an operative of the Spanish CNI (Centro Nacional de Inteligencia). However, the CNI was only founded in 2002. If he truly was the role model of an 80s action movie star, he would either have to have served in the CESID (Centro Superior de Información de la Defensa) - which is unlikely, given that it was only founded in 1977 - or, more likely, the late Francoist SECED (Servicio Central de Documentación), which existed from 1972 to 1977.
In "Hard Kill", Delorca's character addresses the villain "El Jefe" directly as "El Jefe" - which he wouldn't do in reality, since "El" is Spanish for "The". Then again, "Hard Kill" is just a silly 1980s action movie.