Letter of recommendation from non-native speaker
USA Grad Schools Answer:

Spelling and grammatical errors are ignored - especially if we know the letter writer is not a native speaker. The letters are letters, not published, peer-reviewed journal articles.

What is usually more problematic with academics who didn't come out of American systems (or who haven't been here long) is that they don't fit the genre form of American letters of recommendation - which is excessively flourished praise over several pages with minutiae of biographic details and research insights.

I have read many letters from colleagues at foreign universities that are just three sentences long. This won't work. One of my American colleagues at my previous workplace regularly wrote letters that were 5-6 pages long. I think that's excessive. Somewhere in between is the sweet spot.

If your professor has been here long enough and gone through grad admissions at an American school, they will know what it takes to get in. I wouldn't worry about the grammar and spelling, though. As long as it comes in on letterhead and/or through the portal, we assume it's genuine. And if it's too opaque, we're known to actually phone letter writers to verify the authenticity or clarify the contents of a recommendation.