After finding the bomb, Detective Beckett calls out on her walkie talkie police radio for the bomb squad. In order for her to transmit, she would need to push the PTT (push to talk) button. You can clearly see her fingers are nowhere near the PTT (push to talk) button at any time.
While Castle and Beckett are in the refrigerated shipping container, it shows exposed refrigeration piping. One hole in any of this piping would drain all the refrigerant and stop the refrigeration almost immediately. Beckett would have known this or at least tried it. Additionally, they both should have known that immobility is the worst way to stay warm in a situation like that. Her training alone should have had them running laps. Although this would have increased their rate of oxygen use, this would not be a factor, as a sealed room that large would give them about 3 days of breathable air, and hypothermia would kill them long before that.
When they are looking up the real Kevin McCann's Army file on the computer, they state that he was in the Special Forces. The flash on his beret is for Joint Special Operations Command, however, his beret is the wrong color. It should be green, not black. The black beret has been used for regular army units (non-Airborne or Special Operations) since 2001. Before this, the black beret was exclusive to the 75th Ranger Regiment, i.e. the Army Rangers. Also, his beret is worn wrong. The flash should be straight in the front and the beret should be flat on the head, not lopsided.
When Castle and Beckett arrive to find Amir's wife, they find an agent shot in the forehead through his driver side window. They show a bullet hole clear through the window. Side windows on cars are nearly always constructed of tempered glass, which shatters into tiny pieces when shot. The window would have been disintegrated, not punctured.
Fallon said that, before questioning Radford, he removed the bullets from the clip. As a professional, he should have said rounds from the magazine.
Castle and Beckett find the agent doing surveillance dead in his car. The man appeared to have been shot though the driver side window of his car as there was a hole in the window. The glass in car windows is made of tempered glass and would have shattered if someone had shot a bullet through it therefor there would not have been a hole.