Facebook connect problem

Hello!

I have a big problem with the facebook login on our site. The problem is that lot of the visitors can comment in the name of an admin without logging in to the site. The admin is the same admin everytime. And they see the full admin page. Maybe the problem is because of the cookies that wp sends to the visitors borwser, but I can’t understand how to solve that everyone get his own login cookie.

I hope the problem is clear and you have some idea to solve it! ??