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: 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.
Character mistake: Captain Holt calls the Pimento case "Operation 225641441636324" which he said he arrived by placing a numerical value to each letter in Pimento and then squaring it. But the perfect squares couldn't match up to Pimento since there's only 6 perfect squares and Pimento has 7 letters (plus the last 2 perfect squares don't fit the pattern of the previous 4). Nor is "225641441636324" a perfect square.
Mr. Santiago - S4-E7
Revealing mistake: When Jake is typing on his computer just before Terry talks to him about meeting Amy's dad for the first time, his computer is and remains on the desktop doing nothing. (00:02:05)
Chasing Amy - S4-E17
Continuity mistake: The position of the money Charles puts on Gina's desk keeps changing through the scene.
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)
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)
Other mistake: When Amy reaches down to get the key out of her shoe she literally only bends slightly. There is no way that she could've reached all the way down to her foot, or retrieve the key in the seconds before she gets it. (00:14:30)
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.
Revealing mistake: When Charles shows the picture of the horse and says "look what you get when you search for 'Charles Boyle medal of valor'" he's typed "peanut butter the horse" into his phone.
Character mistake: When Charles is talking about Terry's kids you can see Stephanie Beatriz (Rosa) trying not to completely crack up next to him.
Revealing mistake: When the motor home explodes, the flames from the explosion are CGI. It doesn't look very realistic at all.
Character mistake: When Gina tries to set up Rosa on a date, Rosa mentions the last person Gina set her up with (Justin) was a dork who rode a Yamaha motorcycle. She says "he might as well have picked me up in a station wagon." Rosa's bike is a Yamaha R1.
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.
Character mistake: When Charles gets kidnapped Terry screams out Joe instead of Charles. (00:05:50)
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.
Character mistake: Jake and Rosa are looking around in The Apartment for months. 14 CIS workers are analyzing The Apartment. All of them are looking for a killer who never left The Apartment. Still, in multiple months no-one thinks about checking the person-sized vents. Seems pretty unlikely. Vents are literally the first thing anybody thinks about when people try to disappear. And a vent of this size is a dead giveaway that someone for sure would have checked.
Continuity mistake: The flyers on the top and bottom of the pile Terry is holding keep changing colors.
Casecation - S6-E12
Factual error: Amy is wearing a NYPD detectives badge even though she is a Sergeant at this point in the show. (00:01:00 - 00:21:20)
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.
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.