Premise: I think that SE as a whole is not nice enough. But I also think that the people of SE are in general a great bunch of people. There is a difference in the way that we communicate that creates conflict. I believe that problem is magnified here because this SE is a practical metaphor for the problem. The questions we face here are often times asking how to resolve problems that exist through out the SE format.
And most of it revolves around our individual interpretation of Be Nice.
I also believe that we as a whole would like the site to be welcoming to everyone. We just all need to shift our perspective a little bit to overcome this difficulty. I also believe that just a few minor tweaks can change the entire network into something that is not just Great, but something that is transformative in all of our daily lives. I know that my participation here has definitely improved my ability to communicate. I suspect it has most people.
Specifically these I believe we can address these 2 points:
Be welcoming, be patient, and assume good intentions.
Don't be a jerk.
Is there some way we can slightly alter this to get a more desired result of less conflict, and acceptance of our differences?
Update - RE:
If you frequently see rude/abusive comments, that means the comments aren't moderated well, and that we need to revisit the comment policy and what we'd allow based on be-nice. Same for answers: if they're regularly being used as soapboxes for opinions, you could make a rule that everything needs a back up or is subject to removal (comment source but may be removed as it is a comment)
If you frequently see rude/abusive comments, that means the comments aren't moderated well - This. But the problem is not the moderators but the rules in which we expect them to arbitrate. If we can give the mods a more appropriate set of guidelines, as well as giving the people the appropriate set of guidelines(boundaries) then we can solve this problem, or at least make it more manageable and improve the over all experience. Most of the time comment arguments appear to start over one mistaken interpretation, then others jump in picking sides. If we can stop the jumping in I think we can stop most of the bickering.