In the opening scene three different people - the commanding officer, the officer of the deck, and the diving officer - give, repeat, and acknowledge the order to go to "periscope depth". In contrast, however, in the real world aboard a submarine of the US Navy one does not give an order to "periscope depth" but rather to a specific number of feet (from the surface to the keel) - because the periscope depth varies (even aboard one individual boat) as a function of the sea state at a given moment and as a function of the height of the viewpoint (above the surface) which the conning officer needs or wishes to achieve.
When Sturgis does an about-face after speaking with the Admiral he does the about-face to the left, which is not correct. An about-face is always to the right.