Hamlet seems to have his moments of insanity and his moments of pure procrastination. Which would be the most accurate tragic flaw to place upon him?
I agree that Hamlet's biggest problem at the outset is his maturity. He's 30 years old and struggles to make the decisions that are important to him. He wanted to return to his studies, but let himself be talked out of it for Gertrude's sake. In addition, his self-centeredness created huge issues. He was appalled at how the marriage of Gertrude and Claudius affected him and with no thought toward how it might have been important to Gertrude.
I, too, don't think that Hamlet is insane. I believe that he uses the ruse of insanity to bide his time, observe, plot, and enact his revenge. I think that his tragic flaw is vengeance. As religious as Hamlet purports to be, he should have abided by the teaching from Romans, "Vengeance is mine, I will repay, says the Lord" (Romans 12:19). Shakespeare certainly presents the seeking of revenge as immoral. His other characters who are vengeful (Shylock, Iago, Macbeth--to a point) do not meet with success and experience great loss.
I'll take another approach and say neither. Hamlet has self control and he does not truly procrastinate. If Hamlet had taken revenge in the second act, what would Shakespeare had done for the last three acts? Some delay is necessary. Look at a Clint Eastwood movie. When does he get his revenge, say in the Unforgiven? Isn't it at the end? The structure of a revenge play calls for the revenge to be actualized at the end. Otherwise it turns into something else.
Yes, Hamlet makes sure that Claudius is guilty before exacting his revenge. What thinking person doesn't? Doesn't Othello wait at least a couple of acts to find the "ocular proof" before killing Desdemona? No one calls Othello a procrastinator. Of course Othello was wrong. Hamlet wants to make sure he is right. Who can blame him, especially if you read Othello. Killing an innocent person is an act that has horrible consequences.
So Hamlet waits to make sure that Claudius is guilty. Then he waits to make sure that he exacts perfect revenge. Again, who can blame him. Perfect revenge calls for the victim to suffer as much as those he has inflicted. Sending Claudius to heaven when he is praying is hardly a perfect revenge. We know that Hamlet is religious from Act 1 and we know that his father is in purgatory. Why should Claudius who killed Old Hamlet enjoy the benefits of heaven? Surely Hamlet will have more chances to kill the king--perhaps when Claudius is eavesdropping in Gertrude's bedroom. Aha! Hamlet acts immediately when the opportunity presents itself. Unfortunately, he kills the wrong person. This tragedy happens not because Hamlet is mad or because he procrastinates. It happens because Hamlet acted rashly. He should have checked to make sure the man behind the tapestry was Claudius. But to Hamlet's credit, who else really would have been in the queen's bedroom?
Talk about the age old question! There are literally thousands of pages of criticism written about this very subject. You have to review the play for yourself and think about what CAUSES the results of the play. While it is debatable, I think that Hamlet is only putting on an act of crazy. While he certainly depressed over the state of affairs in Denmark, I don't think he has lost his senses.
That said, I do think this procastination, especially as a result of his over-thinking on things, is a tragic flaw. He even acknowledges that idea in his famous "To be or not to be" soliloquy. I would also suggest that his deep morality keeps him from acting, which results in the end results. There is no easy answer for this one, but I think you are on the right track.
On the one hand, your topic question recalls the comment that Hamlet "is simply not mature. Intellectually or emotionally"(J. Bronowski), and on the other hand the themes of morality and remembrance noted here this autumn. I think that Hamlet could argue that killing Polonius was an act of defense, that is he had no reason to think anyone else was present, not even the King, despite what he says. The morality theme is broached in the first scene. Horatio tells us that the King of Norway was incited "by a most emulate pride" to challenge King Hamlet to single combat. Pride is one of the seven deadly or cardinal sins. Therefore, one might choose that or any other sin and go from there. Remembrance might remind one, as it were, that in ROMEO AND JULIET the tragedy turns pretty much on Tybalt's failure to temper his desire to duel. The arguement that Hamlet should have killed Claudius sooner rests on the idea that as Prince of Denmark he has the authority to do so, which in turn raises the subject of politics. Claudius says: "Come, Gertrude, we'll call up our wisest friends"(4.1.37). It is then a bit sad that Hamlet doesn't discuss his problems with others. As Polonius says: "But yet do I believe / The origin and commencement of this grief / Sprung from neglected from neglected love"(3.1.177-179). The trgic ending, then, results from Hamlet's failure to "act" in accordance with virtue.
I agree with #3 , but, what would you call your tragic flaw? morality? (no sarcasm intended) I have no clue what to call that... especially if its for a literary essay.