On two occasions the admiral, Tim's father, places his combination cap upside down on tabletops; however, in the real world of the US Navy, it is highly unlikely that a professional long-time Naval officer, especially one as senior as a flag officer, would set down a combination cap upside down with the white cover in contact with a tabletop or other surface.
In the opening scene, a USN destroyer is shown at night in heavy weather. All upper deck lights are on, which a real naval ship would never do at night. In addition, the bridge white lights are on, which would blind the bridge staff to the world outside. In the real world, all upper deck lighting would be off (with the exception of navigation lights), and internal lighting would be red or blue, to assist with night vision. There would be no lighting on the bridge at all.
For a while Gibbs speaks to Adm. McGee, Tim's father, in a forceful, aggressive, authoritative, condescending, untactful, insubordinate tone; however, in the real world of the US Navy, even a Gibbs would not speak to a flag officer, especially one with four stars, in such an in-your-face manner, and an officer of that seniority would not tolerate such treatment, not even from a special agent of the NCIS. One simply does not speak to admirals in that way -- not even federal agents -- not even if an admiral is a suspect.
The commanding officer of the fictional ship, a destroyer, is a captain (O-6), and the dead medical officer was a commander (O-5); however, in the real world of the US Navy, it is highly unusual for the skipper of a DDG to be a captain (more likely a commander) or for the doctor to be a commander (more likely a lieutenant).
After Tony hits Wyeth in the stomach with what appears to be a large can of tomatoes, we can tell by the way he's holding the can, and the hollow sound it makes when he drops it, that the can is empty.
In the letter which Admiral McGee wrote to the Secretary of the Navy, he refers to the President of the US as "Commander and Chief" instead of "Commander-in-Chief".