The Sea
The sea is many things to many people. It is a foe (for Chris), a worthy adversary (for Mat), a purifying entity (for Anna). It takes away people and it gives to people. It is what it seems and nothing more; it is duplicitous and its motivations shadowy. These contradictory assessments demonstrate how natural forces are given anthropomorphic associations in order to allow people to tell themselves what they need to—that the sea has cleansed the sin of prostitution, that the sea is the one that broke up a family.
Redemption
Anna is a "fallen woman," besmirched by her sin and, unless redeemed, liable to remain in this state until she dies. But she shows verve and resilience by seeking out her father, hoping to escape the life she fell into, and she further shows a capacity for hope and love when she meets Mat. Technically Mat is the one who "redeems" her, telling her that if she swears that she never loved anyone else and that she does love him that he'll forgive her and marry her, but one could argue it was Anna taking the first steps to leave land and come to the sea that started her along her path.
Gender
As a woman in a patriarchal society, Anna is subject to men's control, oppression, abuse, and judgment. She is considered a "fallen woman" because she is a prostitute, but the men who seek her services are morally unscathed. She tries to make choices for herself and advocate for herself, but her father and lover try to control her. And those men, who for all intents and purposes should be better than her clients, are just as problematic—they fall into paroxysms of grief and rage when they hear of her fate, making it all about themselves and refusing to offer even a modicum of real sympathy or compassion. So while Anna certainly demonstrates feminist tendencies, as she is strong and independent and sassy, she ultimately is controlled by men.
Obligations
Chris has obligations—to his wife, to his daughter, to himself. Yet he chooses to ignore all of them not because he is purposefully cruel but because he is weak-willed and does not want to face the suffering he causes by leaving his family alone without him as he sails the sea. His inability to meet his obligations has ripple effects and can even be said to be partially responsible, if not mostly, for Anna's descent into prostitution. Unfortunately he does not acknowledge any personal failings here and falls back on his blaming of the sea, a convenient scapegoat for someone who has failed to do his part.
Drinking
Though the play is written and set during Prohibition, much of the action of the play takes place in a saloon or consists of characters claiming that they're going to go drink or have consumed drink. O'Neill isn't critical of this pastime, though, and paints the saloon as a comfortable, companionable, and even therapeutic place for the locals. He also doesn't moralize or blame alcohol for anyone's behavior. J. Chris Westgate notes that "These vignettes establish, then, class affiliation for this saloon potentially, for working class saloons in general that was geographical, economic, and even ideological" and that "the saloon... foregrounded the discourse of community in contrast to that of individualism defined by and defining the middle class."
Naturalism
This play is considered a hallmark of Naturalism, a type of literary and theatrical genre in which characters are "types," usually those at the bottom of the social ladder, who are oppressed by social forces beyond their control. Arthur Holmberg writes of Anna, "she looks, talks and acts as if she had just stepped from the pages of a Naturalist novel: hard-bitten, down-at-the-heels, alcoholic, desperate. She comes, of course, from the Naturalists' favorite social stratum: the bottom. And there seems no way up or out." John Gassner writes that the play did not deal with ideas but with "living people trapped by their circumstances" who are "shown trying desperately to wriggle out of a net of fate partly of their own making, partly woven by the environment to which they succumbed, and partly knotted by a destiny undefined but poetically sensed by O’Neill."
Fate
O'Neill asks his audience/reader to consider whether or not the characters are in control of their fates. Read as a Naturalist piece, no, they are not—Anna becomes a prostitute because that is the only thing she could be given the interstices of her class and gender, and she will not be redeemed from this life in any real way. Read as a Romantic piece, no, they are not—the vagaries of nature will prevail, and men will die at the hands of a pitiless sea. But one could also see Anna coming to her father and the sea as a way in which she takes hold of her own fate, leaving the question of control a murky one.