We hear them most often called "Grammar Nazis." But what we have a colloquial term for (at least, colloquial to "Internet English"); the Finnish have a designated word. The word is “pilkunnussija,”
Pilkunnussija's more lengthy dictionary definitions are actually pretty funny:
Noun (Vulgar, pejorative)- A person with exceptional and unnecessary attention to detail. Noun- A person who believes it is their destiny to stamp out all spelling and punctuation mistakes at the cost of popularity, self-esteem and mental well-being.
When you think about it, it's probably something we could use in the English language, especially for the more zealous of grammar correcting Internet users. We all have that one friend whose purpose in life is to correct grammar. Our proposed term in English might be to call them Daniels.