Not everyone agrees on the negative side of Churchill. Why? Because in the first place, Emma was not exactly entangled and the attachment is in everyone's head without actually being reality. (perception v reality)
Secondly he works as a plot-devise for self-gratified Emma. Only with his letter we can get him as a character. Even Knightley whose judgment we all value, does not know what to think after reading his letter and realises that he was predisposed to think ill of Churchill like the rest was positively prejudiced. (predisposition v reality)
As there was no attachment, is there still violation of propriety? That is a problem. One cannot slight another without involving the other in something. As Emma was not involved (she says so herself), Churchill was not exactly at fault. There are people who do like to flirt, but whose flirtations never go any further (Emma). Would Emma have flirted further if she had not been drawn to that? The only one who could really be angry at him was Jane. Why would Emma be angry apart from out of shame for her own blindness?
They went too far with Churchill on several occasions:
1. At his 'proposal' to Emma. It is good that the viewers should think that he wants to propose, but seizing her hand was too much. A man who does not love a woman does not do that.
2. At the ball, he comments on Jane's bad hairdo. This comment, in the novel, was only meant for Emma. When he goes to tell Jane off on her hair, he actually goes to compliment her on it (placing himself conveniently between Emma and Jane).
3. Lying in Emma's lap at Box Hill. A man in love with another who is watching on does not do that.
The original Frank Churchill is much cleverer than this. He only goes for words, never for acts. The only thing that Jane can reproach him with is that he is cowardish (something that Knightley also does), but it depends on what one thinks about money.
There is a sad and selfish side to Churchill, but he is by no means a fickle man.