Can you let us know what version of Joomla you're using? Also, when do you get that error. Is it when you authenticate, on every page of the site, on the front end and admin area, etc?
If you're getting a 500 error, that means the site can't load. We haven't heard from any other users regarding a 500 error, so I don't have much to go on here. If there was a specific error message on the page when that happened, that would help us investigate further. If you choose to upgrade again, you can also set the Error Reporting option in the Joomla Global Configuration area to "All", which may show a more detailed message of why the site won't load.
Finally, if you upgrade and get the error, if you can still access the admin area, please disable the JFBCSystem plugin. That will likely 'fix' the problem, but disable most of JFBConnect. At least that should help get you going though and we'd be able to investigate further from there.