The box that Jamie finds in the pocket of his jacket contains the Honorable Mention medal. This medal is for deeds of valor performed at imminent risk of life or who have been commended for meritorious acts at personal risk, and who are entitled to wear the insignia of their Department as per the Honor Legion of the Police Department of the City of New York. Although Jamie cannot be given this award publicly without blowing his cover, awarding it to him privately would acknowledge his act.
Danny speaks to building inspector Reid about the C of O which is required for the house. This refers to Certificate of Occupancy.
At Sunday dinner with the entire family, Frank says 'slainte' while raising his glass. This word means 'health' in Irish and Scottish Gaelic. It is commonly used as a drinking toast in Ireland, Scotland and the Isle of Man.