I don’t know when you were in college, but today’s students have access to grammar/spell checking assistance in the word processing programs. There should be no reason for very many errors.
Also, I don’t agree that improper usage (such as mixing up their, they’re, their) constitutes spelling errors; it seems to be more of an ignorance of the proper usage and/or laziness to figure out the correct usage.
If news articles are any indication, the auto-correct functions aren’t helping them that much.
I’m guilty now and then of typos and even bone headed misuse here on FR, but not on finished professional product. I consider lightening fast posts like this to be judged a bit differently than academic and professional work.
While I have no problem with "their" and "they're", I find myself constantly misusing "their" for "their". :=)