I'm finding a lot to agree with all over this thread.
I'd rather not limit it to a definition of the word "pedantic" if people don't mind, particularly since people's personal definitions will vary - some will find some behaviour unnecessarily, nitpickingly "pedantic" while others will accept it as the norm. Further, there will be significant grey areas for everyone.
One suggestion I have to make is that an inexperienced F/O will not necessarily appreciate the importance in the mind of some more experienced pilots of particular items, such as XXTSGR's points about R/T discipline.
In my experience, often it is the case that Captains who have a "thing" about one particular aspect of flying have had an incident related to that area in the past, and are particularly sensitive about it. I am not talking about referring to the "Flaps" lever instead of the "Flap" lever, nor about using a finger on the "thumb"wheel, but rather to such areas as use of correct R/T, or particularly briefing on, say, take-off diversion if the departure runway should close in VFR, CAVOK conditions, etc.
This is an excellent topic, and please keep the contributions coming. I would just plead for people not to try to narrow it down too far.