The sun as the first shot of this series, is a tribute to the 1980 film "Virus" (Virus (1980)) that opened in the same way.
The term "Bravo Zulu" or "BZ" originates from the days of nautical flag signaling, when the flag combination "BZ" was shown it was to convey the message of "well done". In modern naval vernacular it is used as a common spoken short-hand way of telling someone they have performed a task especially well.
The Italian cruise ship in episode 1 is actually the retired Cunard White-Star Line RMS Queen Mary, a 1936 ocean liner-turned-hotel offering art deco decor, fine-dining & casual eateries, bars & a spa. She's permanently moored in the port of Long Beach, California and has been since 1967.
Those unfamiliar with naval protocol and tradition might be confused as to why Chandler is sometimes called both "Captain" and "Commander". Chandler carries the rank of Commander, but he is the commanding officer of the Nathan James, and naval tradition is to address whoever is in command of a ship as "Captain" regardless of the rank they carry. In the modern U.S. Navy most small warships like corvettes and frigates are commanded by a Lieutenant Commander, destroyers and submarines by a Commander and large warships like cruisers and aircraft carriers by a Captain.
In the Arctic, XO Mike Slattery states, "I should've taken that desk job in Miami," as in Miami, Florida. This is a reference to the television show, "Chuck" (NBC), in which Adam Baldwin starred as, "Colonel (Fmr. Major) John Casey (real name: Alex Coburn)" of the National Security Agency (NSA). In the show, Col. Casey reconnects with a woman named, "Gertrude Verbanski," (played by Carrie-Anne Moss) who becomes a love interest. In the final season of the show, after Verbanski breaks Casey out of prison and must now go on the lam, Casey leaves Burbank, California to find her in the series finale. She has an office, does business, and--although it is never stated, according to many fans interpretation of the show--is most likely hiding out in Miami, Florida.