I don't correct grammar, except in my head. However when I was engaged in internet dating, the ability of my correspondents to use language well was certainly a factor in my deciding whether or not the communication had any chance of resulting in a worthwhile encounter. It paid off, too - we've been together now for almost eighteen years! I am always surprised at the relatively low level of literacy skills in a lot of Facebook interractions, although not, generally, from people who are friends of mine (ah, but is that my selection process going on again, even for friendships?). However, I almost lost a friend when I asked her to read a draft of my novel to check for any inconsistencies and mistakes when cutting and pasting some sections and she took me to task for what she perceived as my grammatical mistakes. These turned out to be matters on which we completely disagreed with each other. I've been a language teacher and was trained in drafting clear English in a rigorous job before then. I'm having to fight a bit of a battle with the PhD thesis I'm currently writing, as I want to keep it clear and unambiguous but keep being told by my supervisors that my English isn't "academic" enough. Meanwhile an American friend posted a couple of days ago about the misuse of "nauseous" and "nauseated", and yet according to the UK English dictionaries this isn't a misuse, just a different usage.
It's a funny old world.