Three themes are the idea of senseless (or at least relatively) killing, sexuality and greed. These are shown in a number of ways:
Huff shows this first one as he considers the idea of killing Phyllis' husband and thinking only of how to make it work without getting caught rather than actually considering the moral problems of killing another human being.
He also demonstrates the idea that sexual attraction and greed drive this willingness to kill without serious consideration as he tries to follow through on Phyllis' idea that they could live a nice life together if her husband were dead.
Another theme of Double Indemnity is the old familiar one that there is no such thing as a perfect crime. Huff has a big advantage as a criminal because he actually knows the insurance busiiness. It was characteristic of James M. Cain that he understood his subject matter thoroughly before he wrote about it. Huff thinks he has the perfect scheme for collecting on Phyllis's husband's life insurance policy, but he fails to give sufficient consideration to Keyes, the claims manager, who can sense that there is something fishy about the supposedly accidental death. Also, Huff didn't understand the character of the woman he was conspiriing with. Another familiar theme in the novel is that crime does not pay. Yet another is: Murder will out. The joint conspiracy to murder a woman's husband was also used in Cain's novel The Postman Always Rings Twice, although the motive was different.