The nurse at the VA clinic says the victim was given a prescription for Ativan, Detective Green says that it's an antidepressant. Which is incorrect, Ativan is the brand name for Lorazepam, a benzodiazepine-class sedative that is mainly used to treat anxiety, insomnia and seizures, it is not an effective drug for treating depression.
It is unlikely that the US Army would have dispatched a two-star (Major General) to the court proceedings. Such individuals are in charge of facilities or commands and would be far too busy for a simple appearance in a courtroom. More than likely a person of that rank would either have requested a meeting with the District Attorney or summoned someone from the DA for a meeting.
When detective Briscoe see's the Bronze Star medal he holds it up to read the inscription on the back of the actual medal. There is not enough room for inscriptions on the back on Bronze Star.
The funeral for the victim, Joe Eastman, was peculiar. As a veteran, he is eligible for a full funeral service paid for and conducted by members of the US Army. The playing of "Taps" on a tape recorder by a uniformed officer is not the proper portrayal of a funeral for a war veteran.
Detectives in the NYPD do not give orders to sergeants. The way Briscoe and Green talked to that sergeant in the opening was absurdly unrealistic.
The general who speaks with McCoy about the case has a haircut which is barely within regulations.
The same general walks outside of the courthouse without putting on his hat. Military regulations require the wearing of a hat when outside in uniform except under very a specific set of conditions; none of which were met when he was standing outside of the courthouse.