Error 12 - This is an error we're still investigating, but should only be appearing for Korean accounts which are not able to participate in the open beta. If you do not have a Korean account, we're still investigating this issue but suspect it may simply be due to the Battle.net Account services being slammed by the high volume of traffic or a communication issue between the game and account services.
Error 3003 - Click Options, under Account change your region to The Americas. The open beta is only being held on US hardware.
Error 315300 - Ensure you're using your Battle.net account email address to log in, and not your BattleTag. The BattleTag is an in-game nickname, not your account name.
Error 24000 - Once logged in you may run into this error when attempting to start a game. We're aware and are working to resolve it as quickly as possible.