Indeed his mistake is due to arrogance, but not only. At any rate, his knowledge of Jane was superficial. It doesn't matter whether Jane helped her case or not. She clearly didn't. What is the point is that Darcy felt secure in pronouncing an absolute opinion on a remote observation of her smiles, without even listening in to her conversations - let alone speaking with her. And from this superficial evidence, when called upon it, he insists (smirking) that of course he was right (and brags further about his success) and when trying to drive his point home, his best analogy is of a penniless mercenary. All this on remote observation of her smiles.
He truly has no argument. Elizabeth didn't see this, and I speculate it is because she was surprised with him expressing any positive feelings about her. I also do not judge Darcy for not seeing that as his feelings where clearly misunderstood, possibly due to guarding them too well, Jane's feelings might have also been misunderstood by him. And in his case, Elizabeth had way more opportunities and discussions (and a dance!) to get to know him than what he had with Jane (and he never danced with her
) This part of the conversation was later, so it is understandable that he didn't make the connection.
In all this mess of a discussion he made, he conveniently ignores the only serious argument Elizabeth makes, that lack of evidence (of feelings) does not actually mean lack of feelings. All he says on the topic is "mea culpa, you know your sister better, so ok, I accept she has feelings. But my observations were impassionate and reasonable and what would you do with a penniless mercenary hunting down your sister?" Even getting to accept that Jane cared does not make him question his impartial observations and make an inventory of all this proof he had about her feelings that led him to the wrong conclusion (yes, arrogance...) Too bad Elizabeth got swayed by his weak argument, but then again, she's a girl of 20, not a Cambridge-educated debater...
From a story point of view, the dialogue is perfect and anything else (e.g. Darcy seeing his is arrogant or Elizabeth being so quick and alert that she calls him out for his weak arguments) would be (probably) unrealistic. I simply, theoretically, so wish that somebody would (at some point) call out him for the fool he was here.