I'm seeing the same issue. This whole process has been quite annoying and the only information I've seen about this has not been from the game developers. I know this is a free to play game, but they're making it very difficult for me to choose to buy expansions or any other purchasable part of the game.
The OSX installer from the website doesn't work. ( That would be nice information to have on the download page or the support page for that matter). So you can download it from Steam. I did that. That worked fine except for the game wouldn't update. Turns out you have to change the app name to remove the 'TM'. Which, by the way, breaks steam support. ( Side note, Why they decided to put special characters in a file name is beyond me. That's asking for trouble. ) But so what, I make a shortcut to the renamed executable.
So now I'm able to get all the updates ( This took a whole day as it was over 20GB ). I go to play the game a day later and I can't log in. I get a Game Error 34882524.
I really want to give this game a chance, but at this point I'd rather give $15 to Blizzard and actually spend my free time playing.
Game Error 34882524
Can't open the data files. Check that they exist and
that you have the permission to write to them. The
program will now exit.