It depends on
how have you customized the new user registration page.
If you've modified bb_func_regusr.php you are already broke the core file and that means you may break it further. Probably before the condition which says
if ($correct==0) {
you need to put your own piece of code which will perform kind of validation and then set $correct's variable value to any except 0, if validation do not pass. You may put your own warning message under $l_userErrors[XX] of the language pack where XX stays for the error num of $correct.
Also, you may put such validation code as a plugin under bb_plugins_user.php and it could work non-destructive way.