Action, not in-depth emotional discussion, is the name of the game.
Death Note is the story of Light and L, and their battle for the world.
It, in my opinion, wasn't written to dive into the fathoms of morality, the clash of good and evil; the authors repeatedly stated that they left all of these debates up to the reader, and there is little, if any, moralizing.
It wasn't written to explore madness, isolation, genius, moral obligation, or justice; although these form key parts of the characters' personalities and motivations, and one can pick up a good deal of subtext, Death Note just doesn't discuss them.
It wasn't written to explore the intricacies of, say, a codependent's gravitation towards a narcissist; the focus of the story just isn't there, and Light's and Misa's relationship gets but a passing glance.
The audience never sees, for example, Soichiro and Sachiko discussing Light's guilt or innocence. We never see something like Misa witnessing her parents' murders, and the subsequent living nightmare that must have factored heavily into her madness. We never see L face an inner struggle with what is normal and what is not, or what friendship might mean. Clues to deeper issues are woven into the story, but it is left to the reader's imagination to consider them, and a casual reader can easily miss them.
That isn't to say that Death Note isn't an intricate story. It simply leaves large areas of possible commentary blank.
Death Note is here to tell the story of warring factions. The characters, for all of their complications, are more widely sketched than might otherwise be found - the villains, the heroes, the normal guys. The focus of the story isn't really on how they got to those roles.
The focus is on the action.
And there is plenty of action. Tightly plotted, with a labyrinth of twists and turns, Death Note takes the audience through attack and counterattack and counter-counterattack, elaborate planning, decisive execution, and plenty of shocks. Some of it is deliciously over-the-top, dramatic, and stylish. Some of it is poignantly subdued, lingering and sad. The story does mingle themes of good and evil, power and helplessness, victory and defeat, and the message I took away from it was that nothing is ever black and white (besides, you know, "beware of falling notebooks"). It just doesn't discuss these themes at length.
Enjoy it for what it is, then :)