Simon,
There are a few reasons that the email field can show even if it's set to hidden:
1) JFBConnect isn't properly communicating with Facebook. At the top of the page, it should say "Hi Bob" (or whatever the user's name is. If the user's first name is not showing up there, let us know. That's a problem.
2) The user that's trying to register already has an account with the same email address on your site. In that case, the user will have to use a different email address, or use the left-hand side of the form to login and connect their accounts. You can also enable the "Automatically link accounts by email address" setting in JFBConnect which will skip the registration screen if the same email address is found.
3) You've created a template override or modified our view. Can you check if the following file exists: /templates/<YOUR_TEMPLATE>/html/com_jfbconnect/loginregister/default.php
If so, that means you've overridden the layout of JFBConnect for the registration page. If so, you'll need to integrate the latest changes into that file, or simply remove it altogether to use the login/register view that comes with JFBConnect.
Hope that helps get you started. If none of the above seems right, just let us know.
Thanks,
Alex