Péter,
Can you try a few things that may help narrow things down? With the latest 4.2.0 release, we added the option to hide required fields from the registration flow. Unfortunately, I think that may be an error because if those fields aren't filled out, Virtuemart will deny saving the user. With the VM2 plugin, that's not an issue, as it's architected differently. However, VM1 is very picky about user creation. (Not saying you should upgrade, just giving some information).
With that said, can you try one, or all, of the following:
1) Ensure that any fields marked as "Required" in VM have a Facebook Mapping setup for them in the Profiles area.
2) Show the Required fields during registration (or even all), fill them out, and see if the user is created.
3) Mark all fields in VM as not-required that aren't being mapped into FB.
In general, do what you can to test while ensuring the required fields are filled out and let us know how that goes.
Thanks,
Alex