Hamlet is a social problem - how?In which conditions and where?
The events in "Hamlet" portray social dysfunction on all levels.
On the largest scope, there is political upheaval, as Claudius has usurped his brother's place by force. He is ready to do anything to keep things under control, such as paying off Hamlet's former friends to 'do him in.' The seed of corruption spreads beyond the country's borders, as the letter Hamlet carries abroad is the order for his own execution.
Hamlet's family is dysfunctional, as the roles of its members are no longer clearly defined. Besides fraternicide, the imprint of incest creates inter-relational problems, especially between Hamlet and his mother and Hamlet and Ophelia. (There is a an element of displacement or transfer here, where Hamlet blames Ophelia for the conduct of his mother.)
Hamlet's psychological dilemma is the consequence of the irresolution of conflict. Whether he is only feigning madness or has really gone off the deep end is another question; he is in either regard "a social case," an individual in distress because rules of conduct are no longer respected or followed.