When Hamilton (Jack) is dying from the dueling wound, he proclaims that he's glad it happened. Asked why, he says because it will insure he will appear on the $10 bill instead of Aaron Burr.
Jack's joke about "clearing all eight of my sinuses" was a reference to then-current ads for Dristan decongestant.
In the dream sequence, Rochester's name is Trenton, after the city in New Jersey.
Per the title, Alexander Hamilton was the first United States Secretary of the Treasury and a co-author of the Federalist Papers with contained arguments for a strong government at the time of the formation of the American Constituioin. He served with Geroge Washington during the American Revolution and followed him into the first national government formulating the first government banking systems. A political Rivalee with Aaron Burr resulted in his death in along the west bank of the Hudson River on a rocky ledge in Weehawken, New Jersey, a common dueling site in 1804.
Ross Elliott plays Jack's director. A decade earlier, he played the director in the legendary "Lucy Does a TV Commercial" episode of "I Love Lucy."