What are Hamlet's concern with right or wrong in his political issues? I really don't understand what political terms are causing him inner turmoil.
First of all, Hamlet is incredulous that his mother would so soon marry after his father's death since
she would hang on him [his father]/As if increase of appetite had grown/By what it fed on, and yet, within a month--(I,ii,143-144)
Hamlet reflects that his mother is worse than a "beast" lacking reason would have "mourned longer." This new political development of his uncle becoming his step-father depresses Hamlet greatly: "O, that this too sallied flesh would melt,...Or that the Everlasting had not set his canon 'gainst self-slaughter"(130-133) Later, he accuses his mother of behaving shamefully for her age, for she should be past succumbing to "lust."
Another issue that disturbs Hamlet is the political allegiance that Rosencrantz and Guilenstern give to the new king, an allegiance that effects their hypocrisy toward Hamlet as they pretend to come to him in friendship when they are really sent to spy upon him and report what he tells them to Claudius. (II,ii).
These disturbing actions all seemingly in order to be in favor with the new king cause Hamlet much turmoil and depression. His suspicions of political betrayal aroused, he suspects others such as Polonius, whom he stabs while he hides spying for the queen behind a curtain in Act III, scene Iv. Even Polonius's daughter, his love, Ophelia, falls under Hamlet's suspicion.
In his efforts to serve the ghost of his father by learning how King Hamlet has died, Hamlet smells "something rotten in Denmark." This treachery and betrayal by his uncle and his mother respectively as well as the hypocrisy of his friends and respected Polonius are wrongs that cause Hamlet great turmoil in his soul.