Sorry, but that's not even close to the bottom line. Not to come off as harsh, but I don't even know where to begin here.
To start, Faith's killing of the deputy mayor was, yes, an accident. And Buffy said as much the next episode. She said Faith had to take responsibility, but she also said it was an accident. Faith responded by scolding Buffy, then attempting to frame Buffy and pretend it never happened. At the end of that SAME episode, she goes to The Mayor. Everyone tried to help her. Buffy, Angel, Xander, Giles, everyone. She spat on every single one of them, and then tried to rape Xander, who more than anyone else tried to offer friendship to her. The only one who didn't was Wesley. Angel in the mansion or Xander in the motel? That's not extending friendship or understanding? After Faith turns to The Mayor, she kills at least two people, one being a completely innocent college professor. Before that she attempts to have Angel go evil again and kill Buffy. At the end of the day, regardless of the support Faith did or didn't get from the Scoobies (and she got a lot, more than she deserved after she tried to pin it on Buffy), doesn't really matter. It was her decision to go bad. No one forced it on her, there was no soul ambiguity. She made that choice alone.
So come on, this was hardly a single mistake or an isolated incident. Faith completely snaps and pushes Buffy to the brink more than once.
And to say that Angel hasn't contributed to the final victory isn't even remotely correct. For starters, he's already played big roles in saving the world, and will again on his own show. Way down the road, without him in "Chosen", the world ends and everyone dies. Just a few episodes later, he saves Buffy's life several times. And you're forgetting, Angel tried, several times, to help Faith. Really help her, and he would again a season later.
So to say that Buffy hunting down Faith is "cold blooded, premeditated, murder," is a little harsh. I'm not saying it's right, I'm not condoning it, but Faith had more than earned it by that point. Plus, your argument is kind of contradictory. You said that it was "arguably unavoidable" that the deputy mayor gets killed because he's working for The Mayor. Well, so is Faith, in a way more violent capacity, and she far, far exceeded any kind of evil he did. I mean, she was trying to end the world. She had it coming.
First, I don't consider merely disagreeing with me as harsh, as long as you present your arguments logically and in a civil manner, which you have done, and you don't attempt to either insult John Wayne or make fun of my dog. A man has to draw the line somewhere.
We both agree that killing the Assistant Mayor was an accident. Where we differ is that I see Faith's reaction afterward as the reaction of someone who has been faced with a situation that she was totally unprepared for and obviously has no experience handling. She follows the classic steps of a child who does something that she knows was was very wrong (the kind of seriously wrong like when a 6 year old accidentally swings a a baseball bat in the next door neighbor's house and shatters their new wide screen TV) She 1) tries to run away to avoid getting caught. When accused by one who she doesn't see as an authority figure she says "I don't care." Then, in desperation, fearing the inevitable punishment, 2) tries to put the blame on someone else, "I tried to stop her, but it was really Buffy that did it. She's gonna deny it, but I just though that you should know." Then, when her guilt is undeniable, 3) plots revenge on her punishers."Yeah, well, okay, I got caught, but I'm gonna run away and be a roving bandit. THAT'LL show 'em.)
I'm not trying to put all of th blame on Buffy, Giles, or the others, but I still say that they could have handled the situation better.. Buffy was just as much in shock as Faith was, and while she didn't exactly say, "I'm gonna tell on you," that's pretty much what she was ultimately going to do. And I have no doubt that the idea of Buffy doing anything like that never even entered into Giles' mind. If anything like that had happened, she would have gone to him and told him immediately, (just like she did when Angel came back from hell).
How really hard did they try to sympathize with Faith? And for how long? Not hard enough, apparently, or at least they quit trying too soon, because as we all know from future seasons, Faith is basically a decent person who simply panicked and made some bad decisions, fell under the influence of a charming, charismatic, albeit evil, man, and while under his influence, compounded her mistakes. It could just as easily been Buffy in that alley, in the rain, holding a sobbing Faith, but Buffy wasn't the one who never gave up on her.
When I said that Angel didn't contribute that much to the final victory, I was referring to the battle against the Mayor and his minions, not the mythical "Final Victory" or super Armageddon that was referred to at the beginning of the "Fray" miniseries (which I assume that you mean) Sorry for the confusion. As for that one, however, since Joss has confirmed that the final battle in Season 8 was that battle with the outcome changed, I wouldn't be too proud of Angel's major contribution in that one, even though it came quite close to fulfilling the Shanshu prophecy. He did play a major part in the battle on the side of evil.
As for Buffy's actions, she went to Faith's apartment, armed, with the express purpose of either killing her or delivering her to Angel so that he could do the job himself. That's about as cold blooded and premeditated as you can get in my book.
(And, just for the record, let me apologize here if my rhetoric has outrun my logic, but I have to leave now without rereading the stuff I just wrote and possibly editing it. Dentists don'w wait for fan forums.