The hero in a Shakespearan play always contributes in some measure to the disaster in which he perishes. How is this statement true of Hamlet.
I want to know three character traits of Hamlet that lead him to his downfall.
Hamlet contributes to his downfall and the downfall of Denmark in Shakespeare's Hamlet, specifically, by choosing to not seek his revenge and kill Claudius while Claudius is praying in Act 3.4.73-98.
Everyone who dies, from Polonius to Hamlet, himself, would live if Hamlet acted at this moment instead of waiting (except Claudius, the guilty party, of course). And Hamlet decides not to kill Claudius when the king is praying, because he thinks the king is confessing and would therefore go to heaven if killed. Hamlet says:
Now might I do it pat, now 'a is a-praying,
And now I'll do't--and so 'a goes to heaven,
And so am I revenged. That would be scanned.
A villain kills my father, and for that,
I, his sole son, do this same villain send
Claudius is not confessing (adding irony to the scene), but Hamlet assumes he is. Hamlet's Catholic beliefs suggest that Claudius' soul would be clean and pure immediately after he confesses, so killing him at that moment would send him to heaven. Hamlet won't do this.
By refusing to send Claudius to heaven, as Hamlet thinks, he is taking on the role of God, rather than playing the role of avenging son. Salvation is God's business, not Hamlet's. And the cost of this is the bloodbath at the conclusion of the play.
In terms of personality traits, that is somewhat left to speculation. A personality trait isn't necessarily at fault, here. Hamlet doesn't want to send the murderer of his father to heaven. I'll let you decide what that shows about his personality.
Overall, if you need Hamlet's personality traits, some possibilities exist, but they are not necessarily faults. These personality traits may contribute to his demise, but they are not necessarily negative.
Hamlet is too moral to commit the act of murdering a king (a representative of God, according to the belief of the divine right of kings) unless he is absolutely certain of the king's guilt.
Hamlet is not rash, as Laertes is, for instance. Hamlet is thoughtful and contemplative. Though he can feel deeply, he is also rational and reasonable.
Some commentators believe that Hamlet feels he must be proven correct in the eyes of all of Denmark; that he is civic-minded and must be publicly proven to be correct in his actions. Killing Claudius privately at prayer would not fulfill this need.