When Petty Officer Gibson dies during Dr. Scott's vaccine trials, Capt. Chandler comments that he wants her awarded the Navy Cross. While PO Gibson's act of volunteering for the trial is indeed heroic, the Navy Cross is explicitly reserved for heroism during combat action. As such Gibson would not be eligible for the Navy Cross. Instead the Captain would likely nominate her and other trial participants for receiving the Navy and Marine Corps Medal, which is the highest non-combat decoration awarded for heroism .
Early on when a sailor is being asked questions by the ship's "doc," she calls him sir. The "doc" is a chief, and any sailor who has passed basic training knows you never call a chief sir. Only commissioned officers are called sir.