what are the big problems that hamlet has threw out the play?

Answer 1

By his famous soliloquy starting with "To be, or not to be?"
Hamlet questions his conscience, courage and conviction, whether to act or to fall victim to the inevitable disasters about him. Hamlet is considered a universal character for representing this timeless struggle that has plagued the spiritual development of all humanity, as self-aware beings, constantly battling with moral and ethical dilemmas of free will, reason and justice.

If you need specific examples of where Hamlet falters or questions whether or when to act or not (such as whether to kill the villain kneeling in prayer or spare him and wait for another opportunity instead) please look up Cliff Notes for summary of the scenes and events. If you answer in general, you should list examples to back up your conclusion. If your teacher wants concrete examples, I would list as many as I could find, but emphasize the major events as more important to the plot.

Answer 2

Corruption. Hamlet means corruption when he says something like : something is wrong in the state of denmark. Basically, the whole entire play of Hamlet is about corruption within government, or in Hamlet's case, the royal family.