When Jake meets the building manager he says that he is 33. In M.E. Time he says that he is 34.
During his self evaluation, Jake says he has 72 arrests, but during The Bet (2014), the whiteboard shows multiple times he has more than that. It's unclear how he got these numbers.
Gina's apartment is in very good repair, has a loft and is very spacious for a Brooklyn apartment. There is no way the rent for Gina's place can be "super cheap" in relation to her or Jake's salaries, not even in the mid-2010s.
Jake wears many fake commendation bars that are not issued by the NYPD.
When Amy is speaking to Holt in his office at the very end, he lifts his bowl of soup, and the soup is level with no residue on the inside of the bowl. The shot cuts to Amy and back to Holt, and there is now a trail of residue running up the side of the bowl nearest to Holt's face. The shot cuts back and forth again and the residue is gone only for Holt to then take a sip from the bowl and leave the residue trail on the inside of the bowl. The middle shot of Holt must have been from a later take after he'd already sipped from the bowl at least once.
Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals but below the American Flag bar.