I'd argue that the reason the duplicity of the Danish court affects Hamlet is that it creates a real problem about whether you can believe what you see.
O villain, villain, smiling, damned villain!
My tables—meet it is I set it down
That one may smile, and smile, and be a villain;
At least I am sure it may be so in Denmark.
One may smile - and still be a villain. Appearances can be deceptive, so deceptive that even Hamlet had not really suspected Claudius of being the murderer (despite the fact he sort of claims he had - "my prophetic soul"...).
Point being, the audience don't suspect it either. Claudius has been very charming in Act 1, Scene 2, and has shown no real signs of being a sinister, plotting murderer. It's not until his prayer scene that we actually realise that he has in fact done it.
Because Hamlet doesn't trust the ghost. Nor do we:
The spirit I have seen
May be a devil, and the devil hath power
T'assume a pleasing shape ... (2.2.596-8)
The ghost, Claudius, Polonius (who seems a foolish, fond old man, but is in fact a sinister manipulator), his mother, Ophelia (women "jig, amble, and... lisp... nickname God's creatures", and wear make up - a sign that they can't be trusted!) - no-one, apart from Horatio is straightforward and honest.
Duplicity is undoubtedly a theme. And it stops Hamlet from revenging because it's so difficult to see the truth. How can he tell what happened to his father? How can he know?