I've experienced this same problem with a couple of Facebook connect plugins and on a couple of different computers, one running Safari 4 and one running 5.0.1. The plugin works great in Chrome and Firefox.
When I click the Connect button it opens a new window asking to allow Facebook to connect with the website. When I click the allow button the site is opened in the smaller window without scrollbars. In Chrome, that small window closes and you are now logged in to the website.