Other mistake: Danny says "14 years ago today I kissed Linda" but in previous episodes they were celebrating their 16th anniversary.
Other mistake: Throughout the episode, all the interactions with the characters went from day to night except for Commissioner Reagan chaperoning his grandson's class at the museum. It stayed daylight the whole time at the museum. (00:27:14)
Answer: It is the lapel pin worn by members of the NYPD Honor Legion.
The lapel pin is on Danny but not Biaz, why? Also, Baker, Sid, Frank &Garrett wear one. Significance? Are they all the same?
Is the P.C.'s pin different than a legion pin? What are the symbols and their meaning?
I think it may be Masonic?
But why would the mayor wear one?