Twice Harm and Mac address the CO of the frigate as "commander", whereas, according to a long and unquestioned tradition in the US Navy, the CO of a Naval vessel is properly addressed as "captain" regardless of the rank of that person.
The ensign, the shooter, in this episode, says that he has served two months aboard his ship, and that he is "fresh" from the US Naval Academy, yet he wears the surface-warfare insignia. Those "surface wings" are inconsistent with a new officer without the requisite training and experience.
At one point during an establishment shot at sea, one hears an announcement saying, "OOD, report to the bridge". That announcement is ludicrous, because the OOD stands his watch on the bridge. That is his watch station. The OOD at sea is the person in charge of the watchkeeping party on the bridge, and he has a duty to remain on the bridge until properly relieved.
The Secretary of the Navy calls Admiral Chegwidden "Chedwiggen".