Mary, 

Your "serious" essay on Hamlet is mostly very good. The following specific comments are
geared to quotations from your text:

"I’ve married my former sister-in-law, the queen, with mixed feelings of happiness and sadness. 
I know that in marrying Gertrude I’m only doing what all of you have wisely advised all along" 
(Act 1, Scene 2, Lines 5-9).  This is a paraphrase in modern language; the actual text of these
lines of the play is not the same, so it would be better not to cite it this way. And you really
should indicate the source for your modern paraphrase.  

Gertrude "... continues to have faith and, when given the chance, defended his sanity." 
Inconsistent use of tenses.

Hamlet and Laertes "fencing in an attempt to settle their differences" is not a very accurate
description of what they are doing(!) Don't forget that Laertes is essentially plotting with
Claudius so there is another agenda on his side.  Moreover, Hamlet is pretty passive when he 
accepts the challenge for the duel (the "providence in the fall of a sparrow" speech). He does 
not really have any differences to settle with Laertes; he's just letting things play out
as they will by that point.  

"By the end of the play, Ophelia is heartbroken, afraid and alone."  Actually, she has died
by that time.

"He warns her of Hamlets trickery" -- missing apostrophe in "Hamlet's"

By saying this, Polonius is telling Ophelia not [to] trust Hamlet and not
[to] confuse love for lust.  Unfortunately, you need to be very careful about citations to 
actual lines in the play because there are so many different versions containing different 
things.  In the edition of the play we were using this quotation is lines 193-4 in Act 3, 
scene 2.  

Content -- B+

Structure/Mechanics -- B+