I don't want to take issue with the claim that Bogart is the best actor in the cast (review above), but you can't overlook the underrated Fred McMurray (yes, as in Flubber and the TV series My Three Sons). Lovers of the novel will know that it is Keefer, not Queeg (Bogart) who is the real villain. At the end of the day, Queeg is no more than an ordinary man promoted beyond his competence; it is the cynical, superficially witty novelist Keefer who provokes the mutiny, and having led less clever, more honest men to this dangerous end, carefully distances himself from any responsibility. McMurray turns in the slimiest of performances, outdoing even his overbearing bullying boss in Wilder's The Apartment (with Jack Lemmon and Shirley Maclaine). A truly memorable screen villain, all the more powerful for coming from an actor better known for light comedy.
Jose Ferrer, as the defence counsel, Greenwald, deserves an honourable mention as well. No mere two hour film could do justice to the richness and subtlety of Wouk's novel, but this is as decent a stab as you could hope for.