78% of America right now says BLOWN CALL per ESPN.com
2. The White Sox did exactly the right thing. And, as someone else noted, the batter is free to run to first, even if he starts towards the dugout. The rules about baselines only apply once you are in them.
3. The umpire's signals were misleading. It looks to me like his hand signal indicates an "out" versus a "strike 3" call. When they call "out", it's over. I teach my catchers to look back at the ump when they are unsure, and if he is signalling "out" with his hand, then it is an out. This is important if you have runners on and you don't want to have to throw down to first base and risk a bad throw.
4. The catcher was too nonchalant about whether the play was over. Whenever there is a doubt, especially with 2 out and no one on, either make the tag or hold the ball until you are sure, and if you are unsure, throw down to first.
So, there was plenty of blame to go around. It was a combination of unfortunate circumstances, but the blame should be shared by the catcher and the ump.