Tomaz,
I'm not sure what you have running on your site for registration, but it seems like there's another extension that's intercepting the registration process. It could be a captcha field, a registration validation script, a spam checker, or something else. However, on the JFBConnect form, if you do actually enter 2 different passwords, you'll be returned to the same page with (Google Translated):
Entered passwords do not match. Enter your desired password in the Password box and confirm title to re-enter the password confirmation field.
So, when the passwords aren't correct, JFBConnect properly detects it. When they do match, something else is getting in the way.
Can you check what user, authentication, and/or system plugins you have installed that deal with registration or login, and try disabling them. Core Joomla ones shouldn't be the problem, but if you have 3rd party extensions, that's likely the problem.
If that doesn't help, let us know.
Thanks,
Alex