I just tested that by copying my latest couple of replies to Word 2007 before posting them, and it didn't find any problems with my grammar... I would guess that it depends on which grammar-checking engine is being used? If that's the case, Word 2007's grammar checker appears to be pretty good with short sentences then.
I googled for a Firefox grammar checker - there's absolutely no such thing at the moment. As a matter of fact, this very post comes up as the 15th result on Google, so either there's way too little on this topic or we have really good SEO......