The JED uses JFBConnect for their Login with Facebook button
The reason that happens is because of Facebook. "Pages" can't login to sites, Like content, and do many other 'social' activities that are meant for 'users'. So, when you're logged in as a Page, you'll see that "Switch" text prompting you to switch to a 'personal' Facebook account instead of a 'profile'.
On this site, you won't see that text because we're not using Facebook's Javascript button, we're using a custom image for the button instead... it just looks exactly the same as the Javascript button. You can use your own custom image as well by changing the "Facebook Login Button Type" setting in the SCLogin module to 'image' and then supplying a link to the image you want to use.
Just note, other features, like the "Like" button, must use the Javascript version, and so those will still show the "Switch profile" text (and sometimes the glitchy gigantic box you mentioned) if the user is logged in as a Page.
Hope that's not too confusing. If so, or you have any questions/comments, just let us know.
Thanks,
Alex