Audrey, 

Your "serious" essay on Hamlet is excellent.  You have some interesting ideas and have
highlighted some key issues regarding the love between characters in the play.

The following specific comments refer to specific passages in your text (usually the
place that generated my comment is quoted to start):

"The play centralizes around two families."  Word choice -- "centralizes" should be something
like "centers"

King Hamlet's instructions to his son not to take revenge on his mother -- to "leave her
to heaven" is a very interesting point.  It might be that his feelings for Gertrude have
not really changed (if a ghost can have feelings) and that he's saying Gertrude didn't
have anything to do with the evil doings that led to his death.  On the other hand, the 
production of Hamlet that we saw really seemed to show Gertrude as a willing accomplice 
to Claudius, so it's tempting to think Gertrude was involved with Claudius even before
the quick marriage.  But I'm not sure Shakespeare meant to insinuate that. It's also very 
easy to read too much (I probably have done that myself, in fact) into Shakespeare's use 
of the adjectives "adulterous" and "incestuous" with regard to Gertrude.  Take a look at 
the long note about this on page 30 in the Folger Library edition of Hamlet, for instance.   
Those words apparently had somewhat different and more legalistic meanings in Shakespeare's 
time than they do for us.  Some things that we would never call "incest" were thought of
as examples of incest at that time.    

I think it's very natural to read Polonius's attitudes toward his children as love, and 
it's clear that in the production we saw in Fenwick Theater, Prof. Vineberg's portrayal
of Polonius emphasized that aspect of his character.  However, it's good to realize
that other possible readings exist too. Sometimes Polonius is portrayed as a much less 
loving "control freak" and busybody who simply wants dominance over his children for the 
ways they can increase his power and influence in the court.  

"Polonius’ outrage when he discovers his father was killed by Hamlet."  I think you mean
Laertes instead of Polonius :)

"Although all of Hamlet’s actions prior to this scene point otherwise"  word choice "point" 
should probably be "indicate" or something like that.

"Ophelia loves her father more than Hamlet, due to the fact that she obeys her father’s wishes."
Couldn't the fact that she obeys be more a reflection of her general immaturity?  And "due to"
doesn't really work here -- I think you mean something more like "as shown by."

Content -- A

Structure/Mechanics -- A