I'm very situation specific when it comes to correcting people.
In RP, I almost never correct my partners. Only if all three following criteria have been met will I comment:
a) I must care enough about the RP that I want it to improve
b) I must not be emotionally attached so much that I will be sad if my partner quits over it
c) The issue must come up at least every three posts
d) The RPer seems unaware/unconcerned of the mistake. (for example, if xe's dyslexic and gets embarrassed when xe misses a typo, I'd stay shut the Hell up)
In RP-related chat, I'm a lot more willing to correct, though I do it nicely. Not all OOC conversation is expected to be grammatically correct, but I figure most RPers want to write correctly. ^^ I tend to comment only if the mistake is made multiple times, though.
In non-RP chat on the internet, it has to be one of my pet peeves, or in a situation where proper English is expected.
IRL, I'll correct most people if the writing is going to be seen by the public (or at least multiple people) because I think it's better for one person to say something and maybe make them feel stupid than a bunch of people to potentially notice and think the writer is stupid. This goes double for my friends. They've learned not to ask me to proofread their stuff unless they want me to point out all the weird stuff they don't know.
Now, here are my pet peeves:
-allowed/aloud
-pronoun confusion
-capitalization errors
-runon sentences & paragraphs
-wrong your, there, or to
-incorrect contractions
-"I could care less"
And here are a list of things I couldn't care less about (PROFANITY WARNING):
-commas. You have to really fuck them up before they bother me. Personally, I use too many. Why? Because I put a comma where one clause/thought transitions into another. Why? BECAUSE WE FUCKING TALK THAT WAY. Why the fuck would I write differently than I speak? Makes it difficult to read. A half pause is one of the most important ways to separate ideas. For example, the comma before the "but" in my RP-related chat section. Can you imagine what a mouthful that would be? Reading it all at once sounds funny to me, and the half pause helps to separate the idea and get across the effect that it's a supplemental thought to the primary idea of the sentence.
-quotation mark grammar. If you use them and I can tell what's being spoken and what isn't, incorrectly punctuating within/without the marks themselves probably isn't going to bug me.
-tense shift with time shift. I get that you're not supposed to slide tenses, but sometimes in RP or worldbuilding you're speaking of the past and present pretty simultaneously, or panning from one to the other. As long as it's an intentional shift and not accidental, I don't care if you write about a past event and then one in the present and then back to past without any more clear change than the end of a paragraph.
-syntax. Motherfucking syntax. Writing is speech and thought combined. Write the fucking way it sounds right in your head, proper sentence structure be damned. If it conveys the idea better while incorrect, fuck the rules.
Really, I don't see grammar as rules so much as an explanation for what should naturally happen in writing. Breaking a rule is only bad when it prevents oneself/others from being understood or understanding correctly. It's kind of like driving. If you need to speed to avoid a wreck... yeah, you broke the rules, but the rules are in place to prevent wrecks... which you did. Following the rules usually makes things easier for everyone, but the purpose matters more than the letter of the law.
