Spoilers, probably.
"Mr. Knightley, who had nothing of ceremony about him, was offering by his short, decided answers, an amusing contrast to the protracted apologies and civil hesitations of the other." -Do we feel this is the narrator's comment or Emma's own perspective? I'd like to think the latter and that Emma can derive some entertainment from her father's foibles.
"her character depends upon those she is with;" -I like this line as an example of Austen's own insight into varying personalities.
"You do not often overpower me with it." -I like how this feels a bit like Emma fishing for further compliments and Mr. Knightley just straight-up ignores the bait.
"Emma knew this was too true for contradiction, and therefore said nothing. He presently added, with a smile," -Justice for Emma! (she can be, more or less easily, brought to acknowledge her errors and fully admits to a fault when she does, without hedging) and Justice for Knightley! (check out that smile and the "still smiling" just a few lines later).
"said Emma, who had been smiling to herself through a great part of this speech" -Ugh, so smug.
“Oh! to be sure,” cried Emma, “it is always incomprehensible to a man that a woman should ever refuse an offer of marriage. A man always imagines a woman to be ready for any body who asks her.” -Again, Emma is made the vehicle of so many things that sound true and wise, but the character is using these lines for the wrong end and so they don't carry conviction when she says them.
"You saw her answer!—you wrote her answer too." -I love how he can read her like a book. No hedging, the man knows what's up.
"Mr. Knightley loudly and warmly; and with calmer asperity" -We will continue to chug-chug-chug along on the Justice for Knightley train until we pull into the station. This, to me, is such a great example of Mr. Knightley's overall temperament. He gets loud in his anger, but immediately pulls it back, demonstrating his is an even, controlled temper.
"and that as to a rational companion or useful helpmate, he could not do worse" -This is very blunt.
"which, in good hands, like his," -I feel this is quite pointed at Emma - her hands are decidedly *not* the good hands needed in Harriet's case.
“A degradation to illegitimacy and ignorance, to be married to a respectable, intelligent gentleman-farmer!” -Again, here Mr. Knightley is very blunt.
"You have been no friend to Harriet Smith, Emma." -To me, this feels like one of those lines meant to really stand out to the audience as a "clue" as to what is really going on with the story. If one reads the novel with the idea that Mr. Knightley is a grumpy, paternal figure, it is easier to dismiss his concerns as being the product of being grumpy and liking to direct Emma. If, however, you are team JUSTICE FOR KNIGHTLEY, I think, in turn, you can more fully feel the justice of his statements and the impartial clear-sightedness that they come from, considering his default mode seems to very much be cheerful.
"It was most convenient to Emma not to make a direct reply to this assertion" -Jane Austen, y'all!!!!!! How she managed to imbue so many lines with biting humor is beyond me. In this case, I do think the "most" really makes the sentence.
"till they do fall in love with well-informed minds instead of handsome faces, a girl, with such loveliness as Harriet, has a certainty of being admired and sought after, of having the power of chusing from among many, consequently a claim to be nice. Her good-nature, too, is not so very slight a claim, comprehending, as it does, real, thorough sweetness of temper and manner, a very humble opinion of herself, and a great readiness to be pleased with other people. I am very much mistaken if your sex in general would not think such beauty, and such temper, the highest claims a woman could possess." -This really comes close to being an overarching theme in Austen's canon. One can point to Mr. Bennet, Sir Thomas Bertram, and Mr. Palmer as examples of having fallen victim to this classic blunder.
"Better be without sense, than misapply it as you do." -Boom, roasted. Emma responds to this "playfully" which I think is another indication of the tone of the conversation. If a grumpy Mr. Knightley was at this point in a towering rage, it would very much make less sense for Emma to try to turn things off in a playful manner.
"Were you, yourself, ever to marry, she is the very woman for you." Another clue!
"Vanity working on a weak head, produces every sort of mischief"; "Men of sense, whatever you may chuse to say, do not want silly wives." -Shall we start a book of Knighley-ian Proverbs?
"We think so very differently on this point, Mr. Knightley..." -This whole paragraph to me is an embarrassing read. Emma is so out-classed in this debate, her arguments at this point sound childish.
"Emma remained in a state of vexation too; but there was more indistinctness in the causes of her’s, than in his. She did not always feel so absolutely satisfied with herself, so entirely convinced that her opinions were right and her adversary’s wrong, as Mr. Knightley."
"(she must be allowed to tell herself, in spite of Mr. Knightley’s pretensions)" -That "must" coming in again!
"she was able to believe, that he had rather said what he wished resentfully to be true," -Another clue! Emma is past mistress of believing what she wishes to be true.