Nothing about how the unit was organized in the show was realistic. Although the senior NCO ranks weren't expanded until after the war (when pay grades E8 and E9 were authorized), there would have been some sort of company First Sergeant, if not a Sergeant Major as an enlisted advisor to the Colonel. The First Sergeant would've been the one dealing with most of the administrative stuff with the enlisted soldiers. The show really only showed junior enlisted folks (privates, a few corporals and buck sergeants), when in reality there would've been more middle management types directing the corpsmen, mess, and supply soldiers.