[TorpX]

When correcting towards a course, the sub's actual heading is accurate, however the 'own ship' icon (and thus the plotter) never quite finishes turning to the correct heading, usually stopping about a half-degree short.

I believe what you are describing amounts to, for lack of a better description 'sloppy helming'. The rudder movements, and the resulting turning effects, are not instantaneous. The helmsman must gradually ease the rudder as he approaches the desired course, then at the right moment bring it amidships. Were he to wait until he was at heading X deg., the ship would continue to turn some, and would come to X + 1, or X + 2 deg., which is not what we would want. To put it another way, the turning ship has a certain rotational momentum, and this makes perfect precise helming difficult.