Corrected entry: In S04-E09 (Kill Shot) we see Beckett in her bra looking in a mirror at the scar on her chest where she was shot. Yet when she goes undercover in this episode to a cocktail party in a low cut dress, the scar is gone.
Correction: Since the dress was low-cut, it is a possibility that Beckett simply put make-up on to cover the scar. It would stand out at the party so maybe she would've decided to just cover it up.
Correction: She deliberately calls him "Castle" because he made the kind of statement normally made by Castle. You can tell her meaning from the tone of her voice.