My thoughts:
As someone who has dealt with constant flaming since joining the board, I'm just going to put out that I don't care anymore that I get flamed. I've learned in the course of five months that it's part of being on the forum, and I've stopped letting it bother me. Setting aside my drunken report of the first Battle of the Forum Members, I haven't really been bothered by the flaming, and I've learned to make rational responses to things that seem malicious without getting BAAAAAW-ey.
I think that anyone who joins this board and has a shred of common sense regarding the Internet can also learn to put up with the acidic nature of this place. If they can't put up with it, then they'll eventually leave. We're not going to change who we are just because some noobs complain about us.
As for the issue of people trolling and BAAAAAAAW-ing, like Alexis, I think that there needs to be more oversight on the total picture of different events. Regarding Joe getting banned, I personally don't think the ban was justified since he did not do anything to directly attack Alexis. The picture he made was something that any other /b/-tard would have immediately jumped all over. I think we need to expect the output of this place to be only marginally better than 4chan, because frankly, that's the mindset of the people we have here. And as for Alexis, I've witnessed him troll his way into more flamewars than I thought possible in just five months, and I think he should have been banned after the one last month when he started criticizing Allie/Xanina for her preferences/thoughts about guys. His behavior is attention-seeking, immature, and it takes away from everyone's experience here. If he keeps it up, he should be permabanned. End of story.
So that's what I think.
Short version for those who think it's tl;dr: People who join the board will learn to put up with the bullshit or they'll leave. Don't let new members BAAAAAW-ing derail the board. And people who constantly troll the shit out of threads and then BAAAAAAAW about getting flamed (like Alexis) should get permabanned.