Hmm has anyone selected their character to login with only to get a black screen right after that stayed that way and nothing happened? Is it another common error or did my game just freak out when trying to login
Not exactly, but I am stuck in a perpetual loading screen after character select. I found a neat little easter egg (it's not a bug of course) for PS3 at least, if you hit L1+R1+Start+Select it will toggle the spinning icon off and on. Something to do while you're waiting /sarc.
I have found a seemingly slightly reliable way to get around the NA/EU error and actually select my character, but maybe it's coincidence. I have other characters on JP servers that I will try to login as, and after getting a World Full error, or cancelling out of a queue, or doing a logout it seems to get a fresh Lobby Server more than if you just exit back to main.