The battleship in the opening scene is the USS Missouri BB-63. The Lt. is wearing a cap with USS Minnesota BB-65. The Minnesota, BB-22, was operational from 1905-1921. BB-65 was supposed to be the USS Illinois, but it was never completed.
As Harm talks to Saunders in the bar, the camera moves around the end of the bar and two sets of white actors' marks can be seen on the floor.