In the horse carriage scene, Kevin Chapman was actually driving the carriage himself. This scene did not take place in Central Park, but was filmed in Harlem.
The episode takes place during "Fleet Week", an annual tradition where U.S. Navy, Marine Corps and Coast Guard ships returning from deployment dock in major cities' ports for a week. The sailors on board enjoy shore leave, while the ships are often open to the public, and military activities such as air shows take place. The tradition began in San Diego in the 1930's and has expanded to major ports on both coasts as well as in Hawaii. Fleet Week generally takes place in late May.
Just before the end credits, during the Machine's assessment of Root's situation, one of the graph's node is labeled "Global Thermonuclear War", a reference to WarGames (1983).
The episode features a number of familiar nicknames for sailors and Marines, including "squid" and "swab jockey" (for sailors) and "jarhead", "leatherneck" and "devil dog" (for Marines).
At one point, Shaw tells Finch that an operation has gone "pear-shaped". This is a traditionally British expression for a situation that has gone horribly wrong.