The title "Bang Bang Shoot Chute" is a riff of the lyric "bang, bang, shoot, shoot" from a song by the Beatles, "Happiness is a Warm Gun."
Establishing shot of Mr. Kasdan has him recommending a book, "Stick and Rudder". Since 1944 that has been the most respected introductory book on the essentials of flight and flying.
The sentiment Det. Bell expresses regarding a lack of understanding 'why someone would jump from a perfectly good airplane' is very common and something military and civilian parachutists hear very frequently to express incredulity from those who find out about their activities. The phrase "perfectly good airplane" was popularized by if not originated by the movie Heartbreak Ridge (1986) as "jumping out of a perfectly good airplane is not a natural act....so let's do it right and enjoy the view...c'mon." It was further cemented in popular culture by appearing in the original Point Break (1991) as "You're about to jump out of a perfectly good airplane Johnny. How do you feel about that?"
While generally similar to "The Academy" in appearance, the West Point scenes were not filmed at the United States Military Academy.
While the trousers and dress shirt are indeed very similar to those worn by cadets at the United States Military Academy at West Point, (aka USMA) the garrison cap should be grey. Also, members of "The Long Grey Line" wear the USMA crest which is composed of a sword and the helmet of Athena on a background of gold, grey, or black depending on class year (gold for 3rd class, grey for 2nd class, and black for 1st class). Furthermore, the insignia worn by the actor on the show resembles the dress insignia worn by a Private in the US Army rather than a US Army cadet at USMA.