When Jake and Amy are in the warehouse, her bang is visible in one shot and gone in the next then reappears in the next shot till they run off after Minsk.
Lynn Boyle's ring that Jake can't get off is different than the one that is shown being used when Lynn gets married. Jake's ring is thinner than the one shown being put on Lynn's hand.
A local Brooklyn precinct would have zero authority to actively investigate a currency counterfeiting case, a federal level felony, up to and including the attempt to actually engage the suspect.
While telling Jenny Gildenhorn about arresting the counterfeiter, Jake notes that, "One of [his] three jacket buttons is unbuttoned," reasoning that it must have come undone while subduing the suspect. The rules of fashion dictate that the bottom button of a suit jacket always be left undone, so he committed an error in having it buttoned in the first place, not in having it undone after the physical altercation.
When Gina demands he give her the ring, Jake makes a Lord of the Rings joke, a reference which Gina claims she doesn't get because she's too pretty to watch those kinds of movies. In a subsequent scene, while talking to Lynn Boyle, she likens him (among other things) to a hobbit - a fictional, diminutive, humanoid race - created by Lord of the Rings writer J.R.R. Tolkien.
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.