When McHale and Lt. Parker observe Gruber and the other sailors running their "shindig" from inside Capt. Binghamton's office, trees and the sky are visible through the windows that they use. But when they go outside to confront the sailors, the windows on the building are all shuttered from the outside.
The admiral wears the two stars of a rear admiral on his collar points, and his Jeep flies two stars, but his shoulder boards have the three stars of a vice admiral.
When the doctor comes in to Capt. Binghamton's hospital room, he reports that the tests show Binghamton is suffering from "high blood pressure, acute indigestion, hypertension" before Binghamton interrupts him. "Hypertension," of course, is just another term for "high blood pressure" - a redundancy that no real physician would make.
When Parker is hiding the hula girls in the air raid shelter he brushes against the sand bag which moves quite noticeably (so much in fact that he reaches down for it and makes sure it doesn't fall off). The bags are obvious props filled with something other then sand.
When Carpenter asks Binghamton to explain why he blamed the girl in the closet on him to the Admiral, he replies he did it so he'd "think you were a swinger". The term was certainly not used in the 1940's, and very much part of the 1960's. By WesternOne.