Anyone getting these errors should run a ping test to a random website to see your connection before/during/after trying to log in to FFXIV.
I have been doing this and FFXIV seems to be causing a overall connectivity issue when you try to login and you should see your internet connection stabilize once it kicks you or you exit out.

ALSO, I notice now when its a connection issue by simply watching how the Rating Screen and "Square Enix" logo show up before you get to the start button. Both will appear as if they are stuttering or it takes a long time to get to the actual start button.

Please Read:
(If you do see some sort of connectivity issue when doing this, there is a sticky up on the tech support forum regarding ISP's possibly throttling the connection and it maybe related. Please add your info there for visibility)

http://forum.square-enix.com/ffxiv/t...P2P-throttling