From IMDB:

Cast (in credits order) verified as complete

        Stan Laurel        ...         Stan

        Oliver Hardy        ...         Ollie
        Sheila Ryan        ...         Ginger Hammond
        Dick Nelson        ...         Dan Forrester
        Edmund MacDonald        ...         Sgt. Hippo
        Charles Trowbridge        ...         Colonel Ridley
        Ludwig Stössel        ...         Dr. Schickel (as Ludwig Stossel)
        Kane Richmond        ...         Captain Baker

        Mae Marsh        ...         Aunt Martha
        Ethel Griffies        ...         Aunt Agatha
        Paul Harvey        ...         General Taylor
        Charles Arnt        ...         Doctor
        Pierre Watkin        ...         Colonel Wayburn
        Russell Hicks        ...         General Burns
        Irving Bacon        ...         Postman
rest of cast listed alphabetically:
        William 'Billy' Benedict        ...         Recruit at Corral (uncredited)
        Chet Brandenburg        ...         Mess Hall Draftee (uncredited)
        Robert Cornell        ...         Soldier (uncredited)
        Jimmie Dundee        ...         New Recruit (uncredited)
        Edward Earle        ...         War Games Umpire (uncredited)
        James Flavin        ...         Army Captain at White Army Tent (uncredited)
        William Forrest        ...         Army Major (uncredited)
        Bud Geary        ...         Blue Army Soldier on Bridge (uncredited)
        Harold Goodwin        ...         Army Captain (uncredited)
        Bob Hoffman        ...         Soldier (uncredited)
        J. Anthony Hughes        ...         Staff Aide (uncredited)
        Fred Kohler Jr.        ...         Corporal (uncredited)

        Alan Ladd        ...         Soldier in Photo Shop (uncredited)
        Lyle Latell        ...         New Recruit (uncredited)
        LeRoy Mason        ...         Army Captain (uncredited)
        Ivan Miller        ...         War Games Umpire (uncredited)
        Barry Regan        ...         Soldier (uncredited)
        Dick Rich        ...         Army Post Cook (uncredited)
        Cyril Ring        ...         Canteen Clerk (uncredited)
        Walter Sande        ...         Blue Army Soldier Capturing Stan and Ollie (uncredited)
        Tom Seidel        ...         New Recruit (uncredited)
        Charles Tannen        ...         Lieutenant (uncredited)
        Max Wagner        ...         New Recruit (uncredited)
        Basil Walker        ...         Soldier (uncredited)
        Billy Wayne        ...         Soldier (uncredited)
        Dave Willock        ...         Recruit at Target Practice (uncredited)