"write exactly correct at all times as if an English professor with a personal grudge against you is grading your writing"

The problem is what constitutes "correct": without a central government committee locked in a room and deciding what the correct English language is, it's completely left up to petty tyrants who are no more authoritative than you are yourself, although they have earned the privilege of extra enmity and self-appointed righteousness. Choose a common published style manual and stick to it if you're concerned about conveying information in a de facto standardized way otherwise just relax and write.