The amphibious aircraft used for the commando raid appears to be either a Grumman JF Duck or J2F Duck. While variants allowed for 2 passengers, this aircraft could not accommodate the total # in the commando raid.
When Boyington confronts Major Buell in private, he tells him to climb back on board the "C-47" and leave. The transport aircraft he is referring to was indeed called a C-47 by US Army Air Corps. The Navy and Marine Corps designation for that same aircraft was R4D and since it was marked as a Navy aircraft, he should have referred to it by using that designation.
A bar scene in Officers Club shows Navy officers in modern summer white uniforms but with black shoes. Navy officers only wear white shoes with white uniforms. While the Service Dress White ("choker whites") uniform with shoulder boards existed for officers during WW2, the Summer White uniform, short-sleeve open collar shirt with shoulder boards, did not come into use until after WW2.
In the first dogfight scene, right after Pappy flames a Zero, the camera pulls away from a tight shot of him in the cockpit - and as it does,you briefly see that his "Major Boyington" stencil under the canopy and the Japanese flags representing his Kills are reversed / flipped / mirror image.