These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Les Yay: Good God. Emma even says she's interested in Harriet because she's so pretty and passionately insists to Mr. Knightley that no man in the world is good enough for her. Not to mention the wording of Emma's relationship with her former governess.
Rescued from the Scrappy Heap: Emma again. Jane Austen wrote before she started that, "I am going to take a heroine whom no-one but myself will much like."
Values Dissonance: Emma's ignorance of Harriet's rank and insistence that the circumstances of Harriet's birth should not deprive her of the same respect and opportunities open to richer, less-tender-hearted women is portrayed as a bad thing. note In at least one adaptation, Emma lets her imagination run wild and assumes that Harriet's mysterious father is a member of the royal family! This is why she thinks Harriet is suitable for Mr. Elton - not because rank doesn't matter, but because she's imagined a much more illustrious background for Harriet than is plausible. (Mr. Elton would realize that no royal bastard would be enrolled in a school designed to turn out governesses and ladies' maids, but Emma doesn't.)
More an 'unrealistic given the circumstances' thing. Also in-universe Values Dissonance where Harriet's obscurity isn't a problem to Emma but she considers association with Robert Martin demeaning. And another in-universe example in the great respect Miss Taylor/Mrs. Weston garners as a governess versus everyone being very sad about poor Jane having to become a governess.
That has more do with situation. Miss Taylor/Mrs. Weston lucked out as a governess, getting a good rich family that treated her like a member of the family and loving kids THEN marriage. Marriage is highly unlikely for a governess, which is the only way OUT of being a governess. If Miss Taylor was less beloved she would have been shipped out when Emma was sixteen. You get hints of this with Mrs. Elton being very snide about Mrs. Weston because of her background.
Knightley's objection is probably because it's not fair to delude the rather simple-minded Harriet into believing that she doesn't have a problem... in fact, more to the point, to do so while derailing her marriage to a yeoman with whom she would have been perfectly happy. (Even to the yeomanry it would have mattered, albeit not as much- Robert is still a catch, even if he does get his hands dirty.)
For a completely different example of Values Dissonance, it's eventually revealed that Mr. Knightley has been in love with Emma since she was thirteen...at which time he was twenty-nine!
The book's portrayal of "gipsies" is very wince-inducing now. Not only is that term used freely, but they only randomly show up once as a threat for Frank to save Harriet from, and are portrayed as a faceless Always Chaotic Evil group.
The Woobie: Miss Bates is pretty annoying for most of the book, but you want to give her a big hug after Emma insults her.
Author's Saving Throw: Emma got arrested for 'stealing' (in reality, she was using a self-scanner and forgot to scan an iPod case, and the store needed to meet a quota, so she got arrested) and ended up being fired. The fans went berserk, with quite a few questioning why Emma got fired when people like Cameron (who got arrested for a DUI, lied about where she worked and tried to bribe a cop) and Jack Swagger (who got busted with marijuana) are still on the roster. She was subsequently rehired within two hours. That she's the only Australian on the WWE roster and the company toured there just over a month later (with Emma being featured prominently) probably helped too.
They Wasted a Perfectly Good Character: Arguably after she debuted on the main roster. Apparently the idea behind her being teamed up with Santino was that since he's a ditzy comedic face and she's a ditzy comedic face, they'd make a good team... except that hardly any of the fans agreed, because on the one hand, Emma by herself is a fan favourite who is quite capable of getting over without assistance; and on the other hand, while it might have been possible to pair her up with a male superstar in a team that would actually work, Santino is definitely not that superstar. Nobody liked the resulting team, which resulted in the two of them getting progressively less screen time, which just led to fans getting angrier. In the end, it took Emma getting punished for accidentally shoplifting and Santino retiring from in-ring work for her to finally get to go solo.