Hi Alexander,

Unfortunately the recaptcha is not working properly as now I also have it on the "Welcome screen"

Actually that is the mini registration section. If you do not recaptcha to show in the mini registration, you can disable this in the profile type custom field: http://take.ms/RWe7n

I also get a user error message, saying "there is an error in your registration form. please continue registering".

After you disable the setting above, are you still getting this message?

I disabled it for the Mini-Registration (thanks for explanation, now I also now what this is).
Also the error message seems to be gone - lets hope for the best that it stays so, and it is finally really solved
Thanks!

Hey Alexander,
Glad to know the error message is gone. I think it was detecting that a required field in the mini registration was not filled. That is why it displayed the message.
If you do not wish to utilize the quick registration on your site, you can always turn it off at Settings>General>Login
Once you have made sure the issue is resolved, let us know then we can close this thread.