David Paymer is listed in the credits as 'Dr. Frederick Tate' but named onscreen and on the nameplate on his office door as 'Dr. William Tate'.
Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
Santiago is wearing 2 citation bars that are not issued by the NYPD. Also, NYPD regulations require that the American Flag bar be worn as the highest citation bar - something Santiago would have known.
When Terry calls his wife to prove a point about his sex life to Amy he goes to dial his wife's number, which is an unnecessary/impossible action as there is already an active call visible on the iPhone screen with the keypad hidden.
At around 9:22, Sgt. Jeffords (Terry Crews) pulls out his phone to call his wife. His finger moves as if he is dialing her number while the phone's screen clearly shows an in-call display instead of a keypad, indicating that it is just a prop phone.
When going through a list of traumatic events that Jake has experienced, Terry mentions, "the time you were held at gunpoint and forced to write your own suicide note." He is describing the events of Sabotage (2015), but Jake was not forced to write a suicide note, he was forced to record a video confession/suicide announcement that Geoffrey Hoytsman had written for him.