"Casus Belli" is a Latin phrase that literally translates to "a case of war". As an expression it is used to describe an act or event that provokes or is used to justify war. The term first became widely used in the 17th century by several popular writers when discussing the ways governments at the time tried to justify wars that were unpopular with the majority of the citizens, and often had nothing to do with the reasons the government gave as a justification.
CIWS is short for Close-In Weapons Support, for detecting and destroying short-range incoming guided missiles and enemy aircraft which have penetrated the outer defenses. It is known as a point defense weapon ( the defense of a single object or a limited area, e.g. a ship, building or an airfield) as oppose to an area-defense systems, which have a wider range and are placed near or on the object to be protected.
Tavo said "We will no longer cower in fear of your big stick". It is a reference to a quote by the American President Theodore Roosevelt, which in turn is based on an African proverb "Speak softly and carry a big stick".
It seems that there were two Navy boats named after American Presidents from the show, namely Jeffrey Michener and Howard Oliver played by Mark Moses and John Cothran respectively. In the case of the later, it can be seen close to the end of the episode, where a sailor is playing taps on a bugle right next to the docked ship.
Mahan Hall, where Chandler was lecturing Midshipman at the US Naval Academy was named in honor of Alfred Mahan the President Of Naval War College. Mahan, was well-known for his whitepaper "The Influence of Sea Power upon History".
The Nimitz Library found on the campus of the US Naval Academy, Annapolis, was named after Chester W Nimitz, Commander in Chief, U.S. Pacific Fleet and Commander in Chief, Pacific Ocean Areas, commanding Allied air, land, and sea forces during the Second World War. He played in major role in the surrender of Japan, which led to the conclusion of the war.
The trivia item below may give away important plot points.
When Chandler says of the incoming aircraft "Their wings aren't clean", he is referring to the ordnance mounted under the wings. An unarmed aircraft would have "clean wings" -- no mounted bombs, missiles, or gun pods.