From what I've seen, they basically just write terrible "feminist" hack jobs that are largely responsible for the Man-hating-feminazi stereotype. And thus greatly harm the feminist movement as a whole.
They are much worse than The Daily Mail.
You know, they aren't a really reliable source of information, but citation needed for the idea that they're
largely responsible for the man-hating feminazi stereotype, since that term has been around since
1992 thanks to Rush Limbaugh. Perhaps it
actually is an unfounded stereotype, seeing as apparently the person who put the term into common usage was Rush Limbaugh, not some poor young man who had just had it
up to here with all that feminist man-hatin'.
Second of all, I'm not sure where you get off calling them
much worse than the Daily Mail. Yes, their articles often have holes in them, and no, I don't think they're an accurate source of information. They still aren't publishing articles written by unattractive women, talking narcissistically about how much more attractive they are than other people and how they enjoy special treatment, just to create comment wars about how ugly the author is. The Daily Mail is in a special circle of journalistic hell.
As for Harley Quinn, I don't see the issue. The Tom & Jerry level depictions of violence and the darker themes surrounding such violence in a more realistic situation are a big part of what makes both her and The Joker's characters both amusing and absolutely terrifying. Suicide, and the threatening of it, is par for the course for the two of them.
With Quinn, hypersexualization is a big part of the character as well; and it isn't really meant to be sexy, but tragic. From what I recall, after falling in love with The Joker, she gave up a promising life, a good career, and eventually even her sanity, all in order to attempt to get him to love her in return. And yet, at the end of the all that, The Joker sees her as he sees everyone else; simply another piece in his grand game, worth no more than its potential future use. She's been objectified to the point where that's all that is left of herself.
Which could be fascinating if we explored it from within, rather than without, gave Harley Quinn a story where she manages to get out of there, had some sort of story arc, whatever. As-is it's a lot of very fancy explanation for why they get to have a female character on Maximum Objectification Mode.