In "Hamlet," how is the moral order restored?In Hamlet, the moral order is restored. How can this be proven for most of the characters that die?...

Is moral order restored? I suspect Hamlet is more than a black-and-white morality play where good triumphs and everybody lives morally ever after.

There are no only good or only bad characters; Hamlet's not 'good'. His murder of Polonius is unjustifiable, he allows Rosencrantz and Guildernstern to be falsely executed. Even Claudius, the main 'baddie' has a huge long speech where he tries to repent and we see his conscience tortured by guilt and moral indecision. 

O, my offence is rank, it smells to heaven;
It hath the primal eldest curse upon't,
A brother's murder! Pray can I not...

Try what repentance can. What can it not?
Yet what can it when one cannot repent?
O wretched state! O bosom black as death!
O limed soul, that, struggling to be free,
Art more engaged! Help, angels! Make assay.
Bow, stubborn knees; and heart with strings of steel,
Be soft as sinews of the new-born babe!
(Act III Sc III)

Claudius is not evil (a meaningless word), he is a human who committed a terrible murder to attain his desires. His is not punished for this, rather he is swept up by the chaos he unleashes.

At the end of the play, Fortinbras marches in and steals the Crown and Kingdom from all of them. Not because he is restoring moral order, but because he acts on his desires and grabs the nettle unlike Hamlet with his beautiful but crippling introspection. Hamlet is not a morality play. It is a play about human nature.