What social and political attitudes or traditions does Jane Austen wish to change in Emma?

Jane Austen's politics are highly contested (was she high Tory or secret radical sympathizer: see Marilyn Butler on Austen as Tory and the new book by Helena Kelly: Jane Austen: The Secret Radical for Austen as subversive.) While her politics may be ambiguous, we can locate places in the social order that Austen critiques in Emma. 
Austen's text builds sympathy for the plight of poorer gentry women. While Miss Bates is seen through Emma's eyes as ridiculous, we as readers are also shown a woman trying to survive in reduced circumstances who has been rendered ridiculous by a society that looks down on older, poorer, unmarried women (incidentally, Austen herself a single woman, would have been about Miss Bates's age at the time she wrote Emma.) In having Mr. Knightley scold Emma, and in having Emma herself recognize and repent of her cruelty in making a rude comment to Miss Bates at Box Hill, Austen critiques the casual verbal savagery that can make life a misery for women on the social periphery. Her novel at least suggests changes in attitudes and practices.
In making Jane Fairfax a sympathetic character, which she is even as we see her refracted through Emma's eyes, Austen again critiques a society that doesn't take care of poor gentry woman of intelligence, beauty, talent, and grace. Jane's fate is to become a governess, a career which entails social humiliation and which Jane equates to a form of slavery. Jane is "saved" from governessing through marriage to frivolous Frank Churchill, but implicit in the novel is the lack of choice for a talented woman like Jane.
Finally, Austen critiques snobbery. Emma's snobbery in trying to prevent Harriet Smith from marrying the farmer Robert Martin could have had dire consequences for Harriet, an illegitimate child with little money, no connections, and few prospects. Luckily, it all works out for Harriet, but the reader can easily see, if Emma cannot, how snobbery could have ruined Harriet's prospects.