When trying to reach the helio bay Chandler says the storm damage has knocked out internal communications. Yet a few minutes later he is talking on the intercom with CIC.
For being in very rough seas where the ships are pitching port and starboard and from bow to stern, most of the scenes filmed are extremely level. Further, with a storm that close, the crew would have secured everything and equipment would not fall or roll around.
When the Greek frigate shows up on radar the chief petty officer at the radar station says "radar shows new surface contact, bearing 165". However on the radar screen the new surface contact is shown to be at a bearing of roughly 345 degrees on a heading of 140.
No one on the Greek ship seems concerned that a Hydra-class frigate is outgunned 4:1 by a Arleigh Burke-class guided missile destroyer. A destroyer is a larger, more heavily armed ship than a frigate and in addition the Nathan James, being a guided missile destroyer, is designed to intercept and shoot down missiles. Considering that the Greek ship is a standard frigate and not even a guided missile frigate they actually don't stand a very good chance in a fight with the Nathan James.