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.
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.
Character mistake: When Charles gets kidnapped Terry screams out Joe instead of Charles. (00:05:50)
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.