Changing the Primary Domain DNS name of this computer to "" failed.
This is a bogus error message that can be safely ignored - it's caused by the domain join code ending up in a function which it doesn't need to run anyway during a domain join operation using the GUI.
What's failing is the attempt to change the Primary DNS suffix of the machine after the domain join has succeeded - but the Primary DNS suffix is already correct at that point which is why this can be ignored.
The domain join itself is not affected at all and will have succeeded if you're seeing this specific error message with the empty quotation marks as that code is only run after a successful domain join.
As frustrating as it is, this is unfortunately one of those cosmetic issues which aren't likely to be fixed until the next OS version - primarily because it has zero impact and no effect beyond the ugly error message.
A workaround that removes the error message is to populate the Primary DNS suffix of the machine before attempting the domain join.
Footnote: This doesn't repro on Windows 8 or Windows Server 2012
See http://support.microsoft.com/kb/2018583 for further details.