Plot hole: Beckett and Castle lose their cell phones and wallets and are being chased by the mob. Beckett steals a cell phone from a car but can't use it, since it is locked and then shut off remotely. Any cell phone can always dial 911, whether locked or blocked from service.
Continuity mistake: When Beckett and Castle kiss at his party at the end of the episode, the camera is behind Castle, and Beckett's head is leaning toward her left shoulder. When the shot switches to behind Beckett, her head is leaning to the right. Then it switches back to left.
Continuity mistake: After Beckett gets back from her assassination assignment, she washes up in a bathroom and places the gun she was given in her front waistband near her stomach. Then she goes to meet Lazarus (Vulcan Simmons) in the basement, who realizes she's Beckett. When she pulls out the gun, she reaches behind her back to get it.
Continuity mistake: When Lanie arrives at the precinct to check on the baby, her shirt is tucked into her jeans, as seen when she bends over to pick the baby up. When the shot changes to behind Lanie, her shirt is untucked, and then when the shot changes to the front of Lanie, her shirt is tucked in again.