Another place where Hamlet speaks about human weakness is Act 1 Scene 4. He starts talking about the soiled reputation of Denmark due to excessive drinking, but generalizes to a commentary on human weaknesses and their origins.
So, oft it chances in particular men,(25)
That for some vicious mole of nature in them,
As in their birth—wherein they are not guilty,
Since nature cannot choose his origin—
By the o'ergrowth of some complexion,
Oft breaking down the pales and forts of reason,(30)
Or by some habit that too much o'erleavens
The form of plausive manners, that these men—
Carrying, I say, the stamp of one defect,
Being nature's livery, or fortune's star—
Their virtues else—be they as pure as grace,(35)
As infinite as man may undergo—
Shall in the general censure take corruption
From that particular fault. The dram of evil
Doth all the noble substance of a doubt
To his own scandal.(40)
He is listing all the possible origins of human weakness such as nature or habits, but concludes that in the end it doesn't really matter where the weakness comes from. The flaw overtakes the whole of the person. Hamlet reveals his pessimism and philosophical nature. Human weakness is a pervasive theme in this play -- nearly every major speech by Hamlet touches on it.
In Hamlet, human weakness, death, disease, and unnatural relationships are the dominant motifs in the play. The chief crimes in his family, Hamlet says, are murder and incest. He says Denmark is a prison full of spies. He tells his girlfriend (and mother) to go live in a nunnery. So, the play Hamlet comments on the inevitability of human weakness. It's implicit solution, it seems, is to take "arms against a sea of troubles," to fight on even though--in the end--all there is suffering and death. Suffering leads to wisdom.
Here are some examples:
Hamlet originally blames his mother for marrying too soon after his father's death. Her human weaknesses: fear of being alone, adultery, incest, denial of the truth, and disloyalty
He comments on his own weaknesses: too self-absorbed to act; too afraid of suffering and death; too full of conscience
Looking before and after, gave us not
That capability and god-like reason
To fust in us unused. Now, whether it be
Bestial oblivion, or some craven scruple
Of thinking too precisely on the event,
A thought which, quarter'd, hath but one part wisdom
And ever three parts coward,
Hamlet calls himself and others "beasts": cowardly, devoid of reason, base, and easily manipulated. Hamlet sees all too well the human weakness around him. He knows he will be disappointed by others. He knows he will disappoint himself. So, why try? His problem: does he have enough courage to fight against this losing battle?
Hamlet makes a variety of statements about human weakness, at times picking on a certain subset of humanity to do so, namely in his "frailty they name is woman" bit.
In the "To be or not to be" soliloquy he discusses his own and by extension the rest of humanity's inability to act unless driven by some great and powerful emotion. He cannot take certain risks as he isn't sure about the outcomes, if he kills himself will he suffer in hell? If he doesn't avenge his father will it ruin the rest of his life?
If you look closely at his conversation with Ophelia in which he counsels her to get to a nunnery rather than to procreate, several times he makes it clear that he thinks that men are basically only good at vice and sin, even he who is relatively honest and good is guilty of such things as would make everyone blush.
Clearly he does not hold a very high opinion of humanity.