Hamlet Stinks

Got your attention? Good. :) I'm actually referring to the strange obsession with smells, particularly bad ones, throughout the play. Maybe this is a generic high school essay question, but I don't recall ever noticing it before. What's up with the smell?

• "Something is rotten in the state of Denmark." Not technically a direct reference to smell, but certainly conjures up the notion.
  
• "My offense is rank, it smells to heaven..." (Claudius)
  
• "...if you find him not within a month, you will nose him as you go up the stairs..." (Hamlet referring to what will happen to Polonius' dead body after sitting around for a month)
  
• "And smelt so? Pah!" (Hamlet, with Yorick's skull)
  

(Any others I missed? I don't count the Ghost saying "I scent the morning air" because we're talking about bad smells here.)

Do all the latter references exist just to reinforce the "rotten" notion from the opening scene?