In the scene where they are rolling depth charges off the aft deck during a drill, Lee Marvin is first seen as a radio man on the bridge, then after a cut, he is on the aft deck with the depth charge crew.
This movie is taking place during WW2 but the warships are displaying the large peace-time hull numbers, not the war-time smaller hull numbers.
When we first see Gary Cooper he is in a car driving onto a Navy base. There is a guard stationed at the base who waves Cooper in. The guard has a 1911 Pistol holstered on his belt. There isn't a magazine inserted in the pistol so he is guarding the front gate with an unloaded weapon.