Character error
Captain Holt pays particular attention to procedure and yet the holster he wears is incredibly unsafe. It features a thumb-break retention strap that can interfere with drawing his revolver during a confrontation. It also leaves the trigger-guard of his revolver uncovered, increasing the likelihood of a negligent discharge while drawing or holstering, and making it possible for someone trying to take his revolver to fire it in the holster.
Factual errors
CORRECT-GOOF: Holt carries a revolver rather than a semiautomatic like Jake, Rosa, Amy, Charles and Terry do because the NYPD allowed any officer who purchased a revolver prior to the department's switchover to semiautomatics in 1994--such as Holt, who had been with the department since the 1970s--to keep them.