One thing this film showed is that decision-making in tough circumstances is well, tough. Consider the helmsman who didn't know whether to obey Queeg or Maryk. Was turning to the OOD the standard way to resolve such a dilemma or a understandable cop out?
With the duty to obey orders comes the duty to disobey unlawful orders. This puts a subordinate (perhaps young and inexperienced) in a rough spot. What if the lawfulness of the order isn't clear?
Stillwell, the helmsman, probably had no idea how the situation should be resolved. The likelihood of an Executive Officer summarily relieving the Captain -during a typhoon, no less- would've been so remote, it would have never been touched on in any sort of training or ship's orders.
Turning to the OOD -who's nominally in charge of the bridge during his watch- was the logical step in such a chaotic situation. The unlawfulness of the order wasn't clear either. Usually one regards an unlawful order as something blatantly illegal (committing a war crime, etc.); this was simply opposing helm orders. What's more, Maryk was invoking Naval Regulations in relieving Queeg -that would've made it even harder to discern how legitimate his actions were.