Lydgate the sexist

Chapter 27:

"... This play at being a little in love was agreeable, and did not interfere with graver pursuits. Flirtation, after all, was not necessarily a singeing process..."

That line is about Lydgate and his flirtation with Rosamond Vincy.
On her side? She doesn't "distinguish flirtation from love, either in herself or in another". Playing with a woman's feelings places Lydgate in the same group with Willoughby and Henry Crawford.

"Lydgate found it more and more agreeable to be with her, and there was no constraint now, there was a delightful interchange of influence in their eyes, and what they said had that superfluity of meaning for them, which is observable with some sense of flatness by a third person; still they had no interviews or asides from which a third person need have been excluded. In fact, they flirted; and Lydgate was secure in the belief that they did nothing else. If a man could not love and be wise, surely he could flirt and be wise at the same time? [...] The Vincys' house, with all its faults, was the pleasanter by contrast; besides, it nourished Rosamond—sweet to look at as a half-opened blush-rose, and adorned with accomplishments for the refined amusement of man."

That's the way he sees her, a source of amusement.
Go back a little, chapter 16:

"He did admire Rosamond exceedingly; but that madness which had once beset him about Laure was not, he thought, likely to recur in relation to any other woman. Certainly, if falling in love had been at all in question, it would have been quite safe with a creature like this Miss Vincy, who had just the kind of intelligence one would desire in a woman—polished, refined, docile, lending itself to finish in all the delicacies of life, and enshrined in a body which expressed this with a force of demonstration that excluded the need for other evidence. Lydgate felt sure that if ever he married, his wife would have that feminine radiance, that distinctive womanhood which must be classed with flowers and music, that sort of beauty which by its very nature was virtuous, being moulded only for pure and delicate joys."

Lydgate thinks of women the way most Victorian men thought of women.
More about his sexism, chapter 17:

"... it was plain that a vicar might be adored by his womankind as the king of men and preachers, and yet be held by them to stand in much need of their direction. Lydgate, with the usual shallowness of a young bachelor, wondered that Mr Farebrother had not taught them better."

Those phrases "his womankind" and "them" refer to Mrs Farebrother (the vicar's mother), Miss Noble (her sister) and Miss Winifred Farebrother (the vicar's elder sister), all older than Mr Farebrother. Uhm? 
George Eliot drops here and there small, tiny details that expose what kind of man Lydgate is, however good he is in other aspects.

"Certainly her thoughts were much occupied with Lydgate himself; he seemed to her almost perfect [...] How different he was from young Plymdale or Mr. Caius Larcher! Those young men had not a notion of French, and could speak on no subject with striking knowledge, except perhaps the dyeing and carrying trades, which of course they were ashamed to mention; they were Middlemarch gentry, elated with their silver-headed whips and satin stocks, but embarrassed in their manners, and timidly jocose: even Fred was above them, having at least the accent and manner of a university man. Whereas Lydgate was always listened to, bore himself with the careless politeness of conscious superiority, and seemed to have the right clothes on by a certain natural affinity, without ever having to think about them. Rosamond was proud when he entered the room, and when he approached her with a distinguishing smile, she had a delicious sense that she was the object of enviable homage. If Lydgate had been aware of all the pride he excited in that delicate bosom, he might have been just as well pleased as any other man, even the most densely ignorant of humoral pathology or fibrous tissue: he held it one of the prettiest attitudes of the feminine mind to adore a man's pre-eminence without too precise a knowledge of what it consisted in."

Here, the Lydgate- Rosamond thing in a sense seems to mirror the Causabon- Dorothea relationship. Through such unequal relationships, George Eliot demonstrates the consequences of gender inequalities, of the lack of education and other opportunities for women. This topic she has discussed in an essay titled "Margaret Fuller and Mary Wollstonecraft": 
http://jpkc.fudan.edu.cn/s/61/t/96/19/1e/info6430.htm
Let's see what's going to happen to this couple.