Continuity mistake: In season 2 episode 11, Jake is shown doing at least 3 pull ups but in this episode he shows he doesn't know how to do one and Terry has to show him.
Continuity mistake: Just before the end credits, Boyle is walking to his desk and he places his jacket over his chair with his bag on top of the coat. The shot changes to Peralta speaking but then the shot goes back onto Boyle and the jacket has disappeared. (00:20:20)
Continuity mistake: When Jake is talking to Gina about Charles' Christmas gift situation, a female cop is walking out from the rest area twice in one scene. (00:01:55)
Continuity mistake: Because the show is filmed in L.A, the lack of snow in December is very noticeable. When the characters are outside there isn't any snow whatsoever, but when Jake, Gina, and Charles are inside the store, the audience can see the heavy snow and blizzard outside from a large window behind them. (00:07:55)
Your Honor - S4-E18
Continuity mistake: In the cold open, when Jake throws the door handle at the interrogation room mirror trying to break it, the handle bounces off the glass to his right, but when the shot cuts to in front of him to show his reaction, the handle flies off to his left. (00:01:00)
Casecation - S6-E12
Continuity mistake: Jake mentions that he's never wanted kids, however he has mentioned loads of times in previous seasons/episodes about wanting to become a Dad.
Continuity mistake: When Adrian stamps "denied" onto Boyle's insurance claim form, there's blank spots where there wasn't enough ink on the stamp (which would happen because he had the stamp in his pocket for a while). But then when he says "denied" and holds up the form, "denied" is all filled in fully. Also, the red border is lighter and the location has shifted down.
Operation: Broken Feather - S1-E15
Continuity mistake: When Gina makes fun of Boyle for wearing a sweater there is a woman behind her talking to cops, when they zoom out it's a man and it changes back when they zoom back in. (00:12:10)
Chasing Amy - S4-E17
Continuity mistake: The position of the money Charles puts on Gina's desk keeps changing through the scene.
Continuity mistake: The scene where Boyle explains the case for Scully and Hitchcock you can see the same two people walking by the room 3 times, coming from right to left in the background. (00:08:30 - 00:09:20)
Continuity mistake: When Charles approaches Adrian about how much longer he's going to stay at his place, he knocks stuff off the desk leaving a pink folder. After Adrian takes the fork away from Charles' neck, there are now extra folders on top of the pink one.
Continuity mistake: When Jake is explaining why he let Richmond go, the left zip of his hoodie goes from folded out to flat between shots and back again a few times. This is especially noticeable when he says "the old me." (00:18:07)
Continuity mistake: The flyers on the top and bottom of the pile Terry is holding keep changing colors.
Continuity mistake: When Jake and Boyle talk about Jake's Dad, a man (grey clothing and holding a cup) in the background (behind Boyle on the left) walks from the back to the front in the same way in both shots. (01:45:00 - 01:55:00)
Continuity mistake: When Charles is talking to Gina in the break room while wearing the mask, he takes it off. When he says she was being sweet, it's back on.
Continuity mistake: When Jake handcuffs himself to Captain Holt, the cuffs around each of their wrists consists of double metal bars connected to a single bar. The direction of the handcuffs changes a few times, going round their wrists the opposite way, which is quite impossible. Then the same thing occurs when Boyle handcuffs himself to Holt. (00:09:35)
Continuity mistake: When the lights go off after attaching the belt to the ceiling, Holt is interrupted before he finishes the word "winner", however in the flashback he says "winner of the 5th annual-" before being interrupted.
Continuity mistake: When Terry's wife Sharon walks into the station, she's wearing a purple dress. When she announces her water has broken while in the interrogation room, she's wearing the purple dress. After returning from commercial break, she's still sitting in the exact same spot but now wearing a burgundy tracksuit and lavender top. (Perhaps she changed clothes because her water broke however, it's highly unlikely since she is sitting in the same place and doesn't look like she's left the room).
Answer: In reality, the Commissioner is a civilian administrator, appointed by the mayor of New York City. He (as of this writing, the role has always been filled by a man; the show gets that part right) is usually someone who has risen through the ranks of the NYPD, but upon becoming Commissioner, is no longer a sworn member of the force (the highest sworn rank is that of Chief). Since Commissioners are appointed, technically anyone can serve in the position, including Deputy Commissioners (who are appointed, in turn, by the Commissioner himself).
Update: On 1 January 2022, Keechant Sewell became the first ever female commissioner of the NYPD.