After Beckett gets off the phone with Perlmutter, she hangs up the phone with her right hand. It then shows Castle, flips back to her and she has her left hand on the phone, then she's not holding the phone, then back to her left hand on the phone.
When the team apprehends the stalker on the bus, Beckett's grip on her weapon changes. It goes from having the support hand's fingers wrapped around the front of the grip, to under the grip in the next angle, then back to the front again.