Of course. We're always being judged by our speaking and writing, even more so in business communication. It's possible that sloppy grammar might go unnoticed, but it could also be perceived as less professional.

This is a very interesting question. I imagine it's completely dependent upon the reader and the extent to which that one understands and values grammar. Personally, as a teacher and a language nerd, I find myself fighting the tendency to be overly critical of anyone's writing. However, in my experience, most people don't even seem to notice the majority of grammatical, spelling, or punctuation errors. I've noticed this in many areas throughout business. For example, I once worked at a doctor's office that used an electronic form to submit patient's questions regarding medication. One option was labeled "side affects." When I mentioned it at a meeting with management, everyone looked at me as though I had three heads. Despite their educations, none of them realized the error. Many of them weren't even aware that there is a difference between "affect" and "effect."