How important is proper use of English grammar?

This is the body of a rejection letter that I wrote and occasionally gets sent to authors whose papers get rejected. Unfortunately...

I serve as the Editor of your recently submitted manuscript. I am sorry to inform you that I am rejecting it for publication. Your manuscript has numerous grammatical mistakes and nonexistent words that inhibit the ability of a reader to understand your arguments. According to page 23 of the AMS Authors' Guide at http://www.ametsoc.org/PUBS/Authorsguide/pdf_vs/authguide.pdf:

"All manuscripts must be written in the English language. Neither AMS editors nor staff have the time available to edit manuscripts that require extensive grammatical changes, as can sometimes be the case with authors from non-English-speaking countries. While the AMS wishes to encourage the international exchange of scientific results through its journals, it requests that such authors make their own arrangements to ensure that submitted manuscripts are already in correct English. If not, their submissions may be returned unreviewed."

The magnitude and extent to which correct English is not employed in your paper is such that I am returning your manuscript unreviewed, as per the AMS guidelines. Only if your manuscript undergoes significant revision may it be resubmitted as a new article. Should you wish to revise and resubmit your manuscript to any journal, I recommend that you hire a technical editor who is proficient in the English language to improve the manuscript or seek out the advice of a native English speaker who will take the time to provide feedback to you in revising your manuscript. Without either one of these approaches, I am afraid you will find your manuscript rejected by most journals.