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.
Brooklyn Nine-Nine (2013)
1 character mistake in season 3 - chronological order
Starring: Andy Samberg, Terry Crews, Stephanie Beatriz, Melissa Fumero
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.
Jake: Captain, allow me to introduce you to major East Coast arms dealer Dan "Daniel" Valdano. That's right, his nickname is longer than his actual name. Why's that, Terry?
Terry: 'Cause he's a dick.
Trivia: Puzzle master Melvin Stermley is played by Melissa Fumero's real-life husband, David Fumero.
Question: Over several episodes we see Captain Holt in competition with other Captains for the position of Commissioner. However, we have seen several Deputy Commissioners on the show. Is Commissioner a position that only Captains are eligible for? Are Deputy Commissioners ineligible? How realistic is this?
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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.