Mr. Darcy's failures parallels Elizabeth's in regards to misunderstanding and misinterpreting what could be accurately observed.
What are some things Darcy misunderstands and misinterprets?
He misunderstands and misinterprets (1) his social duty regarding Wickham ("[he] confessed that he had before thought it beneath him to lay his private actions open"), (2) his presentation of his nature to people ("His character was to speak for itself"), (3) the effect of his proposal to Elizabeth ("'I shall never forget: "had you behaved in a more gentlemanlike manner."'"), (4) Jane's feelings for Bingley ("'though she received his attentions with pleasure, she did not invite them'"), (5) the effects of marriage into the Bennet family ("its being a degradation—of the family obstacles which had always opposed to inclination").
Darcy has more frequent clarity than Elizabeth.
With perhaps a little more frequent clarity than Elizabeth, there are instances in which Darcy has correct understandings and interpretations of that which he observes. This calls up the question: Why would Austen make Darcy a bit more astute than Elizabeth? It would not be in support of the cultural prejudice against women since part of the thematic intention of Pride and Prejudice is to protest that cultural prejudice. Perhaps Austen's choice represents an accurate presentation of the cultural disparity between the public education and experience that gives men the advantage of wider exposure.
Austen can never be used to illustrate the notion that upper class women were poorly educated, although Elizabeth and Jane do illustrate that upper class women were narrowly educated--narrowly in subject and depth--and confined in experience. This is perhaps the reason Darcy has a few more significant instances in which he correctly understands and interprets what he observes: he has broader, deeper education and experience.
What does Darcy correctly understand and interpret of what he observes?
Mr. Bennet's flaw of satirical parental negligence: "The mischief of neglect and mistaken indulgence..."
Mrs. Bennet's flaw of prideful behavior, impropriety and crassness: "total want of propriety so frequently, so almost uniformly betrayed by [your mother]..."
The meaning of Lady Catherine's failure in her confrontation with Elizabeth: "'It taught me to hope ... as I had scarcely ever allowed myself to hope before.'"
How to correct his behavior after Elizabeth's rebuke and rejection of his marriage proposal: "'I hoped to obtain your forgiveness, to lessen your ill opinion, by letting you see that your reproofs had been attended to.'"
With perhaps as many failings as strengths, why is Darcy so appealing to readers?
Mr. Darcy, who makes such a bad first impression, is one of the most beloved heroes in literature. What makes him so beloved in the hearts of readers?
Of Austen's characterizing techniques, three stand out as especially significant. The first is that, before he has gone along too very far, Austen characterizes him as keenly observant and as having the same serious criticisms of Mr. and Mrs. Bennet that we have (this provides support for the ideas that Mrs. Bennet is not just a foolish character meant for comic relief and that Mr. Bennet is not just a satirical diversion).
The second is that Austen very soon shows him as yielding and able to change. For him, Elizabeth's beauty increases with his appreciation of intelligence emanating from her "fine eyes" and with the thoughtful concern that motivates her otherwise ill-advised walk to Netherfield resulting in her freshened "complexion."
The third and key characterization technique Austen uses in regards to endearing Darcy to readers' hearts is the letter he writes to Elizabeth. Readers feel the sincere transparency of his words. When Darcy finally has a chance to show his improved, inner character, gracious, kind, and ready to help the Bennet family during Lydia's elopement, he is fully immortalized as one of literature's best loved heroes.