Indeed, the analogy speaks of something rotten and usually what rots are perishable goods as fruit, vegetables and meat. The analogy is using the physical metaphor of putrefaction to show that a state can also putrefy, i.e. be corrupted. A fruit is a physical item; a state is a notion that represents men of power organized and in command of others, using the physical and intellectual resources of the state to run the country.
Shakespeare is using this metaphor to show that moral corruption in turn causes physical corruption. Another notion associated with this analogy is the notion of the body politic versus the body individual. The body individual is the body of a person; the body politic is the state (including the King). King Claudius has murdered King Hamlet and King Hamlets body is rotting in its tomb. Because he was the King of the state, i.e. the body politic, the state is dying and it has been Claudius that has infected it with his corruption.
Marcello’s words foreshadow Prince Hamlet’s discovery of Claudius’ crime.
The author is very clear in this sentence. "Something is rotten in the State of Denmark". He didn't say in the country or in the land, but in the State. The political definition of state is <em>"a political organization with a centralized government that maintains a monopoly by use of force within a certain geographical territory"</em>. Something is rotten in the political organization, which is an allusion to corruption.
Third person is when a story is narrated by one of the characters. If you only know the narrators thoughts, then it is third person limited. If you know others thoughts as well, then it is third person omniscient.
