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)
Revealing mistake: At the end, Gina makes her flame-thrower with cologne and lighter. However, she never lights the lighter and the flames still appear, as if they were just added in digitally.
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.