Fred Astaire plays a WWII fighter pilot, although he was 44 years old when the movie was made. A more typical age for a WWII fighter pilot would be half that. Most men who were 44 years old serving in WWII did so from behind a desk.
When Fred's escort in the parade shows him to the door at the hotel, she turns as the hotel room doors open. The next frame, they are back together in their original positions before the door opened. This is supported by the later photo of them that Robert Benchley shows Fred at the bar after creating the Flying Tiger drink.
In the beginning of the film Fred Astaire is shown piloting a P-40 "Flying Tiger" Warhawk. He is in pursuit of a low winged enemy plane. After he shoots a plane is seen going down with smoke coming out but it is a biplane, not the one he was chasing.
During Joan's photo tour of the docks, the docks are gated and patrolled by security due to wartime as unloading of a ship goes on, but Fred manages to get aboard ship and borrow a dolly without anyone seeing him.