The words "nitpicking" and "pedantic" actually define this phenomenon of pointing out others' minor mistakes. I have only this urge to do the nitpicking; I don't necessarily point out that petty mistake but I really have this urge to do the nitpicking and give a damn care to the exasperated sighs.
So, is there a good word for this "urge to do the nitpicking"?
Again, I am not asking for words that define this nitpicking phenomenon, just the urge to uphold it.
Edit (choosing the answer):
I kind of liked the phrase obsessive-compulsive corrector suggested by GMB below... its only shortcoming being its being sort of a medical jargon (as well as a phrase).
Then I rediscovered the term twitch, which relates broadly to my urge.
Ermanen came up with probably the best answer — censorious. At first, I didn't like the word, since it described me as a person who finds fault in almost everything. But I guess I can soften it — "I am just a little bit of censorious."