Trivia: When Captain Aubrey makes the toast 'To wives and sweethearts - may they never meet' he is following a custom in the Royal Navy called the toast of the day. There was a special toast for every day of the week. This one in particular was usually for Saturdays. There is a minor mistake, however: tradition dictated that the proposer (in this case, the captain) would say the first part 'to wives and sweethearts', to which the most junior officer present would reply 'may they never meet'. Here is the list that seems to be most commonly followed dates from before Trafalgar, courtesy of the Canadian Navy website: Monday - our ships at sea, Tuesday - our men, Wednesday - ourselves, because no one else is likely to both, Thursday - a bloody war or a sickly season (to ensure quicker promotion), Friday - a willing foe and sea room (The two preceding seem to be of historical interest only), Saturday - wives and sweethearts - may they never meet (reply is made by the youngest officer present) Sunday - absent friends.
Trivia: The book, from which the film is based, was actually set during the "War of 1812" between Britain and America, and in the book the Acheron is an American made vessel used by America. By contrast, in the film the Acheron is an American made ship used by the French, who are the nemesis of Britain in this film.
Trivia: Paul Bettany describes the scenes in which he collects insects: "I don't like insects. They tend to scamper and scuttle, so it was difficult." He also practiced for his self-operating scene by sitting "at home and [trying] it with a butter knife in front of the mirror."
Chosen answer: The flag is a signal flag, and is probably meant to signal that the ship is a whaler or engaged in fishing operations. Such flags were part of an international code, which, with some modification, is still in use today. (The flag is similar to the modern-day "Foxtrot".)