I don't know if it's as strong as a god-complex, but he certainly believes himself to be above some moral laws in the play. He murders Polonius and feel justified in doing so because he was behind the arras. He feels almost no remorse. He plots a murderous revenge on his uncle without guilt coming into play- his reservations lie in the courage to complete the task at the right time, but not because he is squeamish about committing murder. He certainly believes that he is smarter than the people around him, he is constantly speaking in riddles, knowing full well that no one will understand what he is saying, even though he thinks it's perfectly clear. For example when he is talking about the location of Polonius' body or when he is insulting Polonius to his face.
King- Now, Hamlet, where's Polonius?
Hamlet- At supper.
King- At supper where?
Hamlet- Not where he eats, but where he is eaten.