When on board the aircraft carrier, as "Spig" Wead is leaving the ship, a plane is being towed in the background. The national insignia on the side of the aircraft is incorrect. There was no red stripe in the white bars that bordered the star during WWII. This version did not come into being until after the war.
When Frank "Spig" Wead is taking command of the aircraft carrier during WWII the car that drives up to the docked carrier is a 1950 or '51 Chevrolet or Pontiac yet the scene is supposed to be during the war, which ended in 1945.
When Wead takes the Army pilot for a flight in the seaplane, he uses an electric starter to get the engine going. Planes of that era had to be started by hand-pulling the propeller blades, called "propping," a very dangerous and tricky procedure.
When Jughead is showing Spig the "new" carrier, Saratoga a flight of airplanes goes overhead. The airplanes are Douglas AD-1s (Later A1E). The AD-1 wasn't developed until late 1945 and the first ones were delivered to the Navy in December 1946 - thus, totally wrong for 1927 when the Saratoga was commissioned.
When Jughead is showing Spig the carrier, Saratoga the carrier appears to be a Midway class carrier. The Midway carriers didn't appear until late 1945. Also, the aircraft on the deck are Grumman TBF Avengers and Chance Vought F4U Corsairs - both types were developed in the late 30's - not available in 1927.
When on board the aircraft carrier, as "Spig" Wead (John Wayne) is leaving the ship, a plane is being towed in the background. The national insignia on the side of the aircraft is incorrect. There was no red stripe in the white bars that bordered the star during WWII. This version did not come into being until after the war.
When John Wayne's character "Spig" Wead flies through the hanger in the first flight scene, he's initially flying from the front seat, his passenger (Hazard) ducks into the rear seat. As the plane goes through the hanger the pilot is flying alone, from the rear seat.
There is a drawing of a cowboy's head on the wall outside Dodge's office. It appears in three different places when Wead first meets Dodge. It can be seen initially three pictures from the right of Dodge's door as Wead approaches the secretary, then it is seen on the opposite wall behind Wead when he enters Dodge's office, and finally it can be seen immediately to the left of Dodge's office door behind Dodge's head when they leave the office.
Shortly after Spig rejoins the navy, he is shown reporting on the sinking of the USS Hornet. Later, just before Spig gives a brief overview of the "jeep carrier" idea, the admiral is briefed on the Japanese carriers Akagi, Kaga and Soryu. Clearly he is being informed on the Battle of Midway, where those carriers were sunk. The Hornet had yet been sunk at that tine. It did in fact take part in the Battle of Midway and came through unscathed.
When Wead meets John Ford to discuss film writing, the director has four Oscars in his office. Presumably the date is 1930-31 but Ford's first Oscar for "The Informer" was 1935. His fourth was 1942. Furthermore, Wead already had contributed to three previous films from 1929 onward.
When Wead meets Captain "Jocko" the aircraft carrier bears the side number 3, which was USS Saratoga. Jocko Clark's ship was Yorktown (CV-10), which Wead joined in January 1944. Furthermore, the plane being hoisted aboard is an F4U Corsair, which did not deploy on carriers until December 1944.
When Spig and Dodge are screening the dailies of "Hell Divers", the smoke they exhale goes behind the movie screen on the wall. During the take they were sitting in front of a blank wall and the dailies they were "watching" were added later causing them to obliterate the exhaled cigarette smoke.