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.