tl;dr - Google Drive seems to have a pretty good grammar proofreader, possibly good enough to justify pasting drafts in regularly for a quick analysis.
So I don't really like Google Drive for many reasons. Mostly because I've tried to use it regularly, and if there's one thing Google's really good at, it's keeping people from using their products in new and interesting ways that the developers didn't plan for. Drive is sort of like a Dropbox clone, and better than Dropbox in a few aspects, but in the core syncing bits it's straight up not as good as Dropbox, not does it want to be, it's inferior by design. It's also a decent office suite, but it brings all the same problems as previous office suites, most notably for me, refusal to create or edit text files without converting them to their own pet format first.
The truth is it's not a big deal. Dropbox exists so I don't have to care how good Drive's sync is (or isn't), and I use text editors to do all my writing in, and the few cloud apps I've used are all generally inferior to native apps (and may always be inferior, do you really want the problems and limitations of streaming music and video to be present in the applications you use? Streaming media saves you space, what does streaming apps save you? Marginal space, and it loses you time. They're great if you're traveling though. Then again, so is a flash drive). My biggest problem with Google is they seem to want to steer progress. Compare that with, say Valve, who still steers but also regularly tosses out their own internal tools and lets their users do what they want with them, and use that to inform their own direction.
Trying to steer progress is fine, it's allowed. But it can result in crusades, like ignoring (or actively reducing) the value of microSD storage on mobile devices, or pushing Plus on people---auto creating accounts for users of other Google services, generally seeming hostile to people who just want email or cloud storage and don't want to become pawns in Google's pissing match with Facebook.
Anyway, the thing I wanted to talk about is editing documents in Google Drive. It's just that the five minutes I spent in Drive testing this feature reminded me of all the terrible problems it has. The interface is slow, unintuitive, extra open tabs all over the place which deleting documents won't close for some reason, instead they take me to a different dashboard than the one I started from. Again, I digress.
The spelling/grammar checking is actually pretty good. Good enough to see the error in "Why don't you tell hi that?" (the correct version would be "Why don't you tell him that") That won't pop up as wrong in any spell checkers, and very few grammar checkers will catch it. I'm checking out a lot of other proofreading software, most of which has me wanting to reach through my computer screen and throttle developers.
It's not perfect, and after a few minutes of testing I discovered a few parts where I thought it was being really clever it turned out it didn't know the difference between the right or wrong way after all. It detects most obvious its/it's issues, but it's surely no substitute for an actual human proofreader.
Just the same, I was impressed by it, I'll probably run near-final drafts through it in the future just to see what it picks up.
And btw, it doesn't underline errors in green, but in red, so at first glance it may look like it's not working. And as I said, it does miss some things. But it caught a few tiny errors for me that I may never have caught on my own, thanks to my darned pattern-completing eyes and brain.
Funny side note, I can report that Drive's spell/grammar checker is not present in Blogger, after seeing how it treats the example error which Drive does catch.
Anyway, that's my piece.