Just after the part where Kate goes to call her father after seeing Joe Torre, Kate and Castle are talking to Bobby Fox at the table in his office. As he is talking about the Field being built he's playing with a bottle of water and the black top is on. Camera cuts to a side view of Bobby and he states things hadn't changed as much as he'd hoped for and the top is now gone. Camera cuts to a shot of Kate and the top is back on again. Shortly after, Bobby picks up the bottle and then goes to take a drink. When the camera cuts back to him, the bottle is gone from the desk. He then proceeds, after some dialogue, to get up and walk over to the drinks counter where he picks up a bottle of water and goes back to the end of the desk where he stands with his arms out telling a story. The top is on then it's off then it's back on again. Finally, he sits back at the desk and the bottle is gone.
In the episode "Suicide Squeeze," Beckett says over the phone that her badge number is 41319. However in the same episode and other episodes her badge is clearly visible and has the number 0334.
Cuba does not have a consulate in New York City, or an embassy in Washington, D.C. Instead, Cuba has an interests section in Washington, D.C. and a mission to the United Nations in New York City. Detective Beckett is correct when she states that the head of the "Cuban Consulate" does not have diplomatic immunity, but more limited consular immunity. However, the head of a mission to the United Nations would have full diplomatic immunity.
When they suspect Lara as the murderer, Becket is on the phone and says she wants a TSA hold. After being on hold, she says she wants a detain and contain, and all no fly protocols. She never gives the name of the person. Also, having a hold and detaining her would have been impossible in the first place because at that point they didn't even know her last name.
While Alfredo Quintana is being questioned, he says his alibi is that he was at home with his wife, sons, and brother. Castle asks if there was anyone who was not a blood relative. While his wife is family, she is not a blood relative.