Although a shot and a beer are known as a boilermaker in most of America, what Reese gave Finch was technically called a depth charge, where the shot-glass is dropped into the beer.
A Lockheed A-12 "Oxcart" is visible on the deck of the USS Colorado. The A-12 was a developmental aircraft that was used by the CIA from 1967-1968, and would never have been deployed to an aircraft carrier, especially not in 2013 when the episode takes place. The Intrepid Sea, Air, & Space museum stood in for the fictional USS Colorado, which explains the presence of the aircraft.
The Marine started the bar fight over the sailors using the term Jarhead, but the word was never taken as particularly offensive and has become the more commonly used term over Leatherneck. It definitely was not offensive enough to warrant sober Marines risking getting arrested or even injured over.