As a person who is not totally secure with my command of English, I assure you I check for typos twice as hard for my job applications, including agonising over the choice of US or UK spellings when applying to US MNCs while living in a UK spelling locale.

We ended up hiring several people from outside the U.S. Their resumes were pretty much impeccable.

I know lots of immigrants with excellent grammar and spelling. A few who even bother to get someone else to check their resume for that stuff.

Professional proof reading costs money. If you are modifying your resume for each job you are applying, it will cost you a fortune. And asking your friends who speak English natively(very few immigrants have those) is not so good since most native speakers have grammar problems( unless you have a friend with a Phd in English lit).

You think immigrants can't write English correctly?

Is "people using their second or third language will make more grammatical errors than people using their primary language" really that controversial of a concept?

I wouldn't so much call it controversial as I would call into question its relevance. Most immigrants I've spoken to are very aware of how hard it is to build a career when nobody can understand you. They don't come out and say it, but you get the feeling that they put a LOT of time and effort into learning how to become effective communicators in English. I would expect a foreign applicant to make fewer spelling/grammar errors because of this.

The exception to this is when I find an "enclave" of foreigners all working at the same shop where the boss is foreign as well. English communication in these environments is worse than usual. But meeting random foreigners in places normally dominated by native speakers like coffee shops and bars? You don't want to know how many hours they've put into getting better at English. It will make you feel like a lazy, racist asshole.

People who speak English as a second language very well, in my experience, make fewer grammatical errors than native English speakers like myself. This is because they've taken the time to learn the correct grammar rules, and are also careful to apply these rules in speaking.

This was a problem for me when I took the GMAT exam, because there is a grammar section there that's based on some formal grammar rules that I wasn't aware of. For example, look at the example sentences for Rule #5 at the end of this article: both sentences sound correct to my ear: http://www.knewton.com/blog/gmat/2011/06/14/what-to-memorize...