You could write volumns about Hamlet's problems. Narrowing it down is the tough part. Hamlet is slow to action. His father's ghost asks him to kill Claudius and it takes Hamlet literally months to act. Hamlet goes through a great deal of self-derision over his lack of action and then he doesn't take action until the last scene of Act 5 and then only because the opportunity practically demanded action. Hamlet didn't plan the death of Claudius; the emotion and occasion was just there. Many scholars say that the problem in Hamlet is Hamlet's lack of action. In Act 1, sc. 5, Hamlet says the ghost is "honest", but by the end of Act 2, Hamlet says the ghost may be a "devil" and so he arranges the visiting players to enact the scene of his father's death as relayed to him by the ghost. Even after Claudius reacts after seeing the play and Hamlet is convinced the ghost was truthful in Act 3, sc. 2, Hamlet still delays in killing Claudius. Hamlet compares himself to both Fortinbras and Laertes who are both more determined in their quest for revenge for their fathers' deaths. He notes their action and his inaction - yet he still hesitates. Other problems Hamlet has include the question of his sanity. Is he sane or is his "antic disposition" an act? Another problem is the relationship Hamlet has with his mother. Is he jealous of Claudius marriage to her? Also, Hamlet is not the king; another problem.