I am a stickler for correct grammar and spelling. It really does rub me up the wrong way when people screw it up. However, I have been living in the real world for a long time now and have had to come to the unhappy realisation that most people actually just don't care that much. Me getting annoyed with them doesn't make them care, either. So for the vast majority of the time, I don't bother correcting other people [if I did, I would spend my life doing nothing else].
However, I want to be corrected myself when I screw it up, because it's important to me. And for those of you saying, "Oh yeah, they look really arrogant when they correct themselves with embarrassed emoticons," I have to ask, why is your nonchalance about grammar and spelling more valid than my thinking it really matters? I correct myself because I don't want to present the image to others that I make those sorts of silly mistakes, or that I see them and let them lie. Not because I feel that makes me better than anyone, but because that is who I am.
And for what it's worth, correct grammar and spelling does exist for a reason. I constantly speak in nonsense sentences with words that don't exist when talking to people informally, but I need to know I can do it properly when required [i.e. when I need to get an important point across, or when writing a formal letter or what have you]. What does piss me off is people thinking it never matters, because that's basically condoning ignorance. Like people laughing when they say they're rubbish at basic maths, instead of thinking, "Actually, I'll do something about that, because it is an important skill."
Finally [I don't do succint]: I refer you to the following two sentences:
"Let's eat, grandpa!"
"Let's eat grandpa!"