Awesome, Dear Boy: Although Russell Crowe had reservations about the first drafts of the script that he had been sent, the chance of working with Peter Weir was what ultimately convinced him to commit to the project.
Doing It for the Art: Peter Weir insisted that the production use real cannons firing actual gunpowder charges in order to show realistic recoil and to capture live audio rather than using recorded cannon noises in post production. Weir experienced permanent hearing loss that he attributes to his decision.
Dyeing for Your Art: Jack Aubrey is supposed to be quite stout, and Russell Crowe attempted to gain the necessary weight but found that he couldn't, so the film had to settle for a captain who was slightly overweight. Crowe and Paul Bettany also learned to play the viola and cello, respectively, so that they could be filmed performing the proper bow and finger techniques.
Enforced Method Acting: Much of the filming was done onboard the Rose, a modern replica of the 18th century frigate HMS Rose, which was a semi-contemporary of the real HMS Surprise. All actors were given a crash course on 18th century sea-faring. Also during rehearsals, all actors were given tags based on whether they were officers or sailors. This enhanced the sense of camaraderie within each group, and made sure the actors felt that officers and sailors should not mix. Officers' actors were also given a nice clubhouse to rest in throughout the filming. Notably, Paul Bettany was the only one out of both cast and crew to never get seasick (he had quite a bit of boating and diving experience already).
Stillborn Franchise: The film adaptation had nearly the entire cast signed on for multiple sequels, and they bought the actual boat they used to make sure it was going to be available. It made enough money to be deemed a financial success, as well as being well-received critically, but not enough to make the sequel a sure thing, and in the end it never happened. The principal cast have all said over and over that they'd love to do more, and so has Peter Weir. Weir just tends to take a long time in between his projects. He also said that shooting a film on water is the hardest thing a director can do, and thus he'd really need to be sure that it'd be worth it.