A character says a criminal went to a gun show to buy a gun to avoid a background check. In New York and everywhere else, sales by dealers at gun shows require a background check. It is a very common misconception that gun shows don't require background checks, there was a time when gun shows didn't do background checks, but that was 30 years ago. Even if it had been a private sale not at a gun show, New York still requires a background check. In the real world, criminals that want to use guns often steal them, which negates any background check.
During the pursuit in the storage facility, the agents encounter two units with unsecured doors. In real life, empty units are never left unlocked, to prevent customers who are moving out of their units from dumping unwanted items in the unlocked units. They would be secured with (usually) red lock plugs to signify them as 'unrented'.
The agents see the female suspect at the storage unit and give chase a few seconds later. The facility uses motion-activated lights that remain on for at least 30 seconds after someone enters a hallway. The female suspect jumps out from a dark corridor to fight the female FBI agent. In reality, the path the female suspect took would have been lit up like a directional arrow, making it very easy to track her.