The characters continually refer to their station as a "base." In the Army, they are called "posts", never "bases."
In the first newspaper article viewed on screen, "Make the Most of It in Qangattarsa", Col. Woolwrap's duty history includes "Chorea", rather than Korea.
The first time Rudy enters the cafeteria, he looks at the menu. The word, arctic in arctic puffin pie is spelled a-r-t-i-c.
In the hidden medical ward, a dual trace oscilloscope is being used as a heart monitor. A soldier plays the national anthem on a mini Casio keyboard that has not yet been invented.
The C-47 transport plane that flies in and out of the camp was retired from Air Force service in 1975, four years before the setting of the movie.
While guarding the ammo dump, the rifles carried are clearly shown to be M16A2s. The US Army officially adopted the M16A2 as the general issue infantry rifle in 1985. While in service before this, it did not exist in any form of this shape in 1979. They would have been using one of several earlier rifles or SMGs instead.
At 39.08, Spruance mouths the word "Irene", but there is no matching audio . (after he has entered the quonset hut cave)