One of the themes of this story is the notion of gender roles and roles in a bourgeois, 1950s heterosexual marriage. These roles usually include a man who goes out and makes money while the meek woman stays at home to clean and care for the children. There is nothing inherently wrong with these roles; the problem is that they've been used to suggest that women should not work and/or should "serve" their husbands. During the time this story was written, those roles were overly and overtly romanticized as the ideal roles in a marriage.
When Patrick Maloney reveals to his pregnant wife Mary that he's leaving her, she is shocked, but he does not stop her from getting dinner at this time. Up to this point, the narrator has painted the pictured of that romanticized, bourgeois marriage. Patrick is the domineering, working head of the household and Mary is the subjected, meek woman at home who does not live for herself because that is not her role. She has lived vicariously through her husband:
She loved to luxuriate in the presence of this man, and to feel - almost as a sunbather feels the sun - that warm male glow that came out of him to her when they were alone together.
Patrick is dismissive and condescending in revealing the news that he's leaving her because he thinks that is his role. His coldness reveals the lack of compassion he has for Mary's feelings. He yells at her when she continues to make dinner, saying that he is going out, presumably without her. This is the moment when Mary snaps out of her expected role and becomes the dominant one. Not only does she take control of the situation, but she manages to conceive of a foolproof plan to get away with it by having the policemen eat the evidence. She has shifted roles: from meek to strong and in control.
Another theme is betrayal. Patrick betrayed her with cold indifference. He betrays her in abandoning her, for whatever reason we can only assume. She betrayed him, in a sense, by killing him. They are both clearly at fault, but what is interesting is that although Mary's crime is worse, it is easy to sympathize with her; she had been living in a supposedly ideal marriage but it was a relationship in which she was clearly treated like a servant to her husband.