Using CB 1.3.1, Joomla 1.5.22, PHP 5.2.17.
Here is what I have determined to cause the error.
At the CB configuration, under General tab if you set "Calendar Type" to "Drop-down (+popup) calendar" and under User Profile tab you set "Use new div or old table based views" to "use divs (table-less output)" the use of a REQUIRED date field in the Registration screen will return an error (e.g. it will not be accepted). This occurs at least on most recent Firefox and Safari browsers, I believe Internet Explorer does not have an issue.
To prevent the error from happening, I have set CB configuration "Calendar Type" to "Drop-down (+popup) calendar" and "Use new div or old table based views" to "use tables." With these settings, the REQUIRED date field is accepted at the registration process without error.
Maybe a "bug" or at least some form of conflict problem with the described settings?