The sequence where Robert Downey Jr. is seen hanging from a rope flying across the skies above Thailand including a Buddhist temple was done for real with Downey performing the stunt himself after director Roger Spottiswoode had rejected doing it using such alternative techniques such as blue screen or back projection.
According to Wikipedia, "PepsiCo wanted the filmmakers to use a fictional soda rather than show opium being refined at their abandoned factory. Therefore, the producers added a line about wondering if Pepsi knew what was going on".
The movie is set in 1969. The film was the second movie set in that year that actor Robert Downey Jr. had appeared in in recent years as he had recently starred in a film actually called 1969 (1988) a couple of years earlier in 1988.
The film was made and released about eleven years after the source non-fiction book by Christopher Robbins had been first published in 1979. The book was released about ten years after the events depicted in it had occurred in 1969. The book was one of several published works by the author on the film's subject area.
The "golden BB" that Jack Neely talks about is a slang term referring to a single rifle shot that is so well-placed it can bring down a plane or other aircraft. Such shot is demonstrated in the opening of the film.
The movie was originally developed around 1985 with Richard Rush at the helm as director. The film was intended to be the first comedy about Vietnam but Good Morning, Vietnam (1987) beat it to the screens in 1987. Moreover, the 1979 Australian war movie about Vietnam, The Odd Angry Shot (1979), was a comedy.
On the Special Edition DVD "making of" documentary, there is a discussion as to how much of Air America's plot is true and how much is false. Some of the real life pilots interviewed claim that Air America did smuggle guns and drugs for the CIA while others deny it, saying that the service only shipped food, medicine, and supplies. However, a historian in the documentary asserts that only certain pilots were involved in the illegal activities. The characters of Gene (Mel Gibson) and Billy (Robert Downey Jr.) are a perfect example of this. Gene, who is a bit crazy, cynical, and shady, has no problem getting involved in the illegal smuggling so he and pilots like him would have been used for the real life illegal smuggling. Whereas Billy, who is young, honest, and idealistic, would be used only for the straight supply drops and would not be trusted for such illegal activities.