Clooney refers to the rifle as an "M14". The Rüger Mini-14 is a different rifle than the M14 (used e.g. by the Marine Corps prior to the M16).
When Jack is entering the bar where he receives a letter from a friend, a song is played on the radio. The song is 'Tu vuò fà l'americano' by Italian singer Renato Carosone. It means 'You want to do American' or 'You're an American wannabe', a reference to Jack, who is American, and of course the title of the movie.