There is one part where Hamlet expresses the idea that Claudius took the crown from him, "He...popped in between th' election and my hopes," (Act 4, sc. 2). Hamlet, therefore, might feel a little animosity toward Claudius, even though in Denmark's monarchy, the crown didn't automatically go to the son.
In my opinion, he does not. One who is as indecisive as he proves to be, who waffles back and forth and finds good examples on both sides of the fence why he should or shouldn't act, is stalling. He thinks more than he acts, and a leader or rather a cleaner upper of corruption must be more action. At the very least, he must be a balanced combination of thought and action. Hamlet misses the mark here.