A tragic flaw is the failing of a tragic hero, a character who suffers a downfall through the tragic flaw in mistaken choices or in personality.
Hamlet’s tragic flaw is his inability to act to avenge his father’s death, although it must be said that he has valid concerns that prevent him from knowing how to act as he makes clear when he discusses the nature of ghosts that can be sent to ensnare and entrap an innocent in actions leading to the punishment of Hell.
When the Ghost, his dead father, appears to him and charges him with the arduous task of taking revenge for his most foul murder, Hamlet is compelled to accept the challenge even though he fears to: As a Protestant educated at Wittenberg, the university of Martin Luther, he is forbidden to act in revenge because revenge is for God to take, not humankind.
As the play progresses Hamlet finds it difficult to execute his vengeful task. He is stymied from both sides: He needs proof that the Ghost is indeed that of his father and not some foul fiend of the spirit world, and he needs proof that Claudius is himself truly a foul, murdering fiend in the flesh.
In order to uncover the truth of Claudius's guilt before killing Claudius, Hamlet plans to act crazy hoping it will force Claudius to expose his guilt or innocence. Instead, Claudius chooses to send him to England in an assassination plot.
Hamlet also devises the “mouse-trap scene” in a play that is commissioned to be performed. He asks the troupe of actors to enact a scene similar to how Hamlet envisions Claudius's regicide murder his brother and Hamlet's father, Old King Hamlet.
In the final analysis, Hamlet’s tragic flaw, his inability to decide--about the Ghost and about vengeance--and then to act to take revenge for his father’s death, leads him and many others, including his mother, Polonius, Laertes and Ophelia, to their bloody graves.