With Satellite Weather data, RADAR, GPS, all sorts of web based ship traffic position data, etc, it would seem that it is still a much more dangerous business than the Cruise Lines would lead one to believe (not including hiring cowboys as Captains - not that there is anything wrong with cowboys, they just shouldn't be allowed to drive the train...).
Well given the number of vessels that are out there your bound to have problems - the main driver is lack of proper maintenance on breakdowns - one thing the Navy did right in my mind was a solid preventative maintenance system. After that the major issues become mental mistakes - often driven by alcohol and drugs (it can get lonely on the high seas, but even there modern conveniences have eliminated the majority of past concerns with dvds, video games, some oilers have swimming pools for gods sake). Third I would say is improper training or overly quick promotions.
As to the cruise liners I think the big thing to worry about is the airborne pathogens - I’ve heard of more than a few cruises where 1/2 the people onboard got sick. They tend to keep a good clamp on that news with vouchers for another cruise provided you sign an agreement to keep quiet.... but every once in a while it gets out in the press.