Poor Duncan. It is hard not to feel sorry for him given the kind of characters that he is up against. This scene is very crucial for gaining an understanding of Duncan, because he is rather too honest about his own shortcomings. In particular, one of the more revealing comments he makes reveals his own tendency to be taken in by appearances rather than reality, which is ironic given that he is just about to do exactly the same thing, which will lead to his death. Note his comment about the former Thane of Cawdor and his relationship with him:
There's no art
To find the mind's construction in the face:
He was a gentleman on whom I built
An absolute trust.
Duncan clearly is a very naive and gullible King, as the way that he was taken in by his former treacherous Thane of Cawdor amply demonstrates. He appears to lack the necessary political Machiavellian mind to operate well in a position of power. However, he is clearly presented as a very kind, generous and loving monarch, eager to award faithfulness in every way that he can. Note how he responds to Macbeth's arrival in this scene (ironically coming straight after the quote above, indicating the way in which Macbeth will be misjudged by him too):
The sin of my ingratitude even now
Was heavy on me. Thou art so far before,
That swiftest wing of recompense is slow
To overtake thee: would thou hadst less deserv'd,
That the proportion both of thanks and payment
Might have been mine! only I have left to say,
More is thy due than more than all can pay.
Duncan is shown in this speech to be a noble monarch, eager to give Macbeth the reward he deserves for his acts of valour on the battlefield.
Overall, then, we can argue that Duncan is presented in this scene as a generous, kind and loving king, whose fatal weakness lies in his naivety and gullibility and his inability to differentiate between appearance and reality.