In Shakespeare's Hamlet, the one thing about Act Two, scene two, that confuses me is how Claudius can allow Polonius to be his advisor when the man seems so pompous and full of himself, and actually provides little valuable guidance and advice to the King. If Polonius were employed by someone else at the castle, this would make sense, but it does not make sense that the King would allow Polonius to work for him, or that he could be patient with the old man when he begins to ramble and waste the King's time.
If I had the opportunity, I would ask Claudius about this. I would ask if there wasn't someone else who might have been more helpful, especially because Claudius has been King for only a short time. Another man might have been able to give Claudius more advice about how to deal with Hamlet, rather than spying on him. He might even have advised the King to convince Gertrude to send Hamlet back to school, avoiding the "revenge" issue with the ghost of Old Hamlet. (If Polonius were not his advisor, then he would not have been where he didn't belong later in the play, and would not have been killed. In this way, neither Laertes or Ophelia would have died.)