I've tried to access your site but failed. However, I have suspected that the error is because of the 'fullname' field. Did you disable the fullname field from appearing in the mini registration? Because Joomla set the Fullname as a compulsory field in registration hence, it will throw error if the field is empty.
I've re-checked your site and I've turned on this option: http://screencast.com/t/4oLXqwF2QcE and the registration works: http://screencast.com/t/OX3GHSDg . The issue is because this field is disabled hence, Joomla will throw error because the fullname field is empty. Fullname field is compulsory for Joomla user registration.