It will point out mistakes like:
- Use of bad constructs.
- Use of repeated words.
- etc.
(On a side note: if you happen to be a C programmer, I am looking for lint for writing).
No, since writing is a very subjective thing, and many rules rarely work in real life. Thats why I always turn off the grammar check in Ms Word, as it blindly tries to apply some "rules" to everything I write. Like this article says:
Sadly, writing tutors tend to ignore this moderation, and simply red-circle everything that looks like a passive, just as Microsoft Word's grammar checker underlines every passive in wavy green to signal that you should try to get rid of it. That overinterpretation is part of the damage that Strunk and White have unintentionally done.
You are better off allowing other human beings, rather than computers, to critique your work. You can post small snippets here on Writers exchange(subject to these rules), while websites like Critters allow you to post longer works for critique.
Most word processors will pick up things like repeated words, misspellings, and some grammar issues (e.g. sentence fragments; the wrong form of there), but beyond that, they aren't going to be able to catch much else. Things like Lint and FxCop (for .Net) are able be more prescriptive because there are fewer rules in the languages they deal with than in English.
Writing is a far more subjective endeavor than development. A compiler can only deal with its finite set of rules, but a reader can interpret a much wider range of styles.
For the German language something like that exists. The text processor Papyrus Autor does that by following the marking rules from Andreas Eschbach.
But if you write in German or not, you do need that tool, you can make the checks by hand. Yes, it is more cumbersome, so what. Who said writing is easy? If you are interested in the rules, I summarized them in this answer: Marking steps by Andreas Eschbach.
Keep in mind that a marking does not mean, you have to get rid of it. They are just indicators. There are good reasons to kill stuff, there are good reasons to leave it as it is. Rule Number One: Think for yourself.
Aside from the grammar checker in MS Word, I can't really think of any. There just isn't a good substitute for another person to read your work and critique/edit for you.