The essence of this delightful comedy is the English class system that was of the time. The film's added ingredient, that makes it so watchable, is aspiration. The twin themes of class and aspiration also run throughout the sub-plots.
Driven by his desire for success, John Mills' Clifford Southey models himself on James Mason's suave Brett Aimsley, imitating his smart dress, polished speech, and his sophisticated upper-class manner. But Southey frequently reverts to type whenever pressured: as a colonel reprimanding a junior fellow-officer Southey, having worked his way through the ranks, loses his charming manner and barks "get your 'air cut"; later in Tahiti Southey forgets himself when dealing with Marcel, the French policeman, and his flashes of uncontrolled temper and charmless outbursts land him even deeper in it. On each occasion Southey recovers and, as he has trained himself to do, quickly re-adopts the persona of Aimsley to dig himself out.
Southey will never quite achieve the confident, effortless, upper-class charisma that Aimsley exudes in spades - after all it's down to breeding. Captain Aimsley easily disarms Southey's best-rehearsed dressing-downs: "That's Philpott - I take it the firm has lost her too?" exclaims Brett as he notices a picture of the Colonel's wife upon his desk; "But I interrupted you, do forgive me". Brett's innocent interruption blunt his Colonel's attacks and render him lost. Throughout the film, Aimsley stems Southey's flow with such polished interjections.
Ironically, Southey's real persona isn't all that bad: a mixture of gritty determination and acquired manners, he has the right blend for success - no wonder he's the MD! During the scene in which he wins over his fellow directors he mixes the rounded vowels and confident line borrowed from Brett: "Gentlemen, don't do anything I wouldn't do, which of course leaves you free to do absolutely anything"; with the steely flash of quick-fire rhetoric "We've always seen stumbling blocks as stepping stones...". Just like any successful Yorkshire businessman!
So much for the main plot - Mills' character envies Mason's class, and strives to adopt what he can never quite have. But throughout the sub-plots there run similar themes: Belle Annie badly wants to be someone else; alternating between an English lady and an American model, either of which would be a step up the social-class ladder. Because Brett shows little sign of returning to England, her attentions switch to Joey, an American sailor halfway through his Charles Atlas course, who might just help her achieve her secondary ambition of treading the New York catwalk. What aspirations!
Of course, Joey himself has his own agenda, albeit a rather simple one: he wants to be a lover-boy; his womanising desires do not extend to carnal lust - what he really wants is to be an object of desire to like the body-building hunks in his muscle-magazines. A Cassanova image would elevate his status among his fellow crew-members, so he adopts the posturing style of his magazines to win the girl. Too busy showing off his muscles, and expounding his adopted morals, to notice Belle Annie offering herself to him on the beach, Joey finishes up satisfied with his newly-acquired status with his Captain ("What a Cassanova you turned out to be").
Still on sub-plots, what about Herbert Lom's (nowadays)politically incorrect Chinaman, Chong? Clearly he desires the girl, Belle Annie, and does his devious best to win her from Aimsley. But Chong's duplicity when dealing with everyone from American Tourists ("White trash!") to his Anglo-French card school ("All white Christian visitors are welcome on the island") reveals a toadying character to his masters and social betters. He imitates their good manners and behaviour in their company, whilst secretly despising them ("Their white skin! Urgh! And the Smell! Pooh!). Of course Chong can never be anything other than what he is - he is as restricted by his own background as is Southey, "that little clerk".
Look closely and you see other characters whose aspirations cause them to mimic others' behaviour. Roy Kinnear's Captain Enderby, of working class background but elevated army status, has adopted the clipped tones and lofty manner of his Colonel; and the French policeman Marcel's comical literary aspirations cause him, when dealing with Aimsley, to behave as he believes an English gentleman should behave (and relax the law). But Marcel reverts to type and becomes as difficult as any French official when dealing with Southey, who, makes the mistake of rudely declaring Marcel's novel childish.
So the sub-plots mirror the main theme of the film: class, and aspiration. There's a certain vanity throughout, which causes everyone to adopt out of character behaviour.
And Aimsley himself? Mason's character seems at first to lack any social agenda, money aside; perfectly assured and satisfied with his effortless Tahitian life. Yet he too has a secret aspiration - observe how he gazes wistfully at a plane flying overhead; and the fond way in which he reads trivia from his English newspaper. Like Ronald Biggs, Brett Ainsley longs to return to England. What sets him aside is that he will not pursue his particular aspiration - unlike others in the cast - because he has been "cashiered, disgraced" his class and breeding render any such return out of the question.
This doesn't preclude Aimsley from having a little sport with Clifford Southey, by allowing him to shoulder the blame for the attack (and thus pay-back some humiliation and disgrace on his former colonel) even after the penny has dropped that his attacker must have been Chong. Southey, angry and uncouth, departs the island but then (in the final twist), copy-catting Brett Ainsley to the last, takes it on the chin with a civilised farewell wave.