My take:
The slide:
Austin slid 1) too late, going well past the bag and 2) cleats up, right into Holt's ankle. Holt had the right to bark at him for a relatively dirty slide. What should have happened next is Austin saying "my bad." But instead, he barked back. In my opinion, that's already two strikes on NYY (dirty slide, then refusing to apologize). Thus, he probably deserved to get beaned in the back at this point. Saying "my bad" later in the game probably would have gotten him out of a future HBP. However, he continued to act like a punk.
I didn't find it necessary for the dugouts and bullpens to empty after Holt/Austin barked at each other. Being at the game, it seemed like the NYY bullpen cleared well before the Sox bullpen. In fact, the NYY bullpen catcher was well ahead of everyone else, which seemed odd since he looked like some scrawny 20-year old who had nothing better to do.
The hit by pitch:
I personally don't care if it took two attempts to hit him. The player who deserved to get beaned shouldn't "get away with one" just because the pitcher has poor aim. The other thing I noticed is that the NYY dugout was already running out onto the field before Austin charged the mound. It seemed like he was going to charge anyway, but still, the NYY dugout was clearly nudging him on.
Vazquez probably should have grabbed Austin, but at least he pulled his jersey right before he got to Kelly. Who knows, maybe Kelly told him before the inning to let him charge so he could get a punch in. Nothing crazy happened in the brawl as only Kelly and Austin threw punches. Although, Phil Nevin was acting like a nut case and barking at Cora.
Post-game:
Kelly said the right things in the post game (cold weather, bad aim, ball slipped). Of course we know that is a lie, but he has to lie in order to avoid getting a lengthier suspension and fine.