It is interesting that the show uses M1903A3s -- I seem to remember that BoB was pretty accurate as to weaponry - M1A1carbines, no bayonet lugs, etc. I did spot a later M1 Garand rear sight screw and gas caylinder lock screw, but I thought that was forgiveable.
I don't get TV cable and will have to wait until the series comes out on DVD.
P.S. The Army had M1s much earlier than December, 1942. The 164th Infantry Regiment arrived at Guadalcanal in October, equipped with M1s. The problem they had was that an unattended M1 had a tendency to "walk off"!
The marines were reequipped with M1s after leaving Guadalcanal at the end of 1942.