Right now, there's a but in the CB profile plugin where even though the required fields are shown, we're not checking that they are fully filled out. If a user doesn't fill out any of the fields, CB will not properly save the user. It's something we're working on, and will have a fix out once available.
Until then, our best recommendation is to not make many, or any, fields required. If you have fields that are selection types (radio, select, etc), make sure a default is set on them, so that if the user doesn't select something, a value will be there.
That's the best we can say for now, and we hope to get you fixed up soon. Sorry for the inconvenience.
New registration problems
