From 39:51 to 40:56- When Alex is first put in the van she stretches her arms forward to prevent falling. The arrangement of her shackles changes several times between scenes.
At the range, one trainee on the phone walks across the firing line. No Range Safrty Officer would permit this.
The FBI Academy has grooming and dress standards. As such, Simon's and Booth's guy perpetually in need of a shave stubble and Parrish's unbuttoned shirt would not be tolerated. Additionally, the female trainees would be required to wear their hair pinned up.
At 06:47- Since Ryan Booth arrives late to the swearing in ceremony he has not taken the oath as is required by law enforcement officers.
Red handled guns are used to visibly demonstrate a training weapon is being carried. As such, a trainee would never be permitted to leave the firing area carrying an operational gun as it would be clearly visible.
One character says that the CIA is blaming the bombing on "Ukrainian nationalists". However, the nationalists in Ukraine are pro-West and pro-American. It's the ethnic Russian separatists in Ukraine who are opposed to the US.
When Parrish is told her gun had been fired, the Agent says "three bullets." Bullets are projectiles. When referencing a weapon that has been fired, the term used would have been "three ROUNDS."