Aaron,
I'm not having any difficulties visiting your Facebook App page anymore. When I go there, the page automatically logs me in and I don't get any error pages in the process. Things work normally after I'm logged in as well.
I just accessed the admin area to confirm that Conservative Caching was still enabled, so I'm not seeing what you're seeing anymore. I was able to easily recreate the problem previously though.
If you still have the problem, can you try:
* Clearing your browser cache or even try from a new browser altogether. I'm using Chrome on a Mac.
* Try from a different computer
* Try using a different Facebook account
* Going along with caching, I noticed the "shlib - Db query cache and programming library" plugin. I've never seen that, before. Is that something you use, and is it necessary? Disabling that may make a difference (less caching always causes less issues).
Try the above and let us know what configurations do/don't work for you. Since we can't recreate now, we need you to help us narrow down things that may be different between how we're testing.
Finally, caching definitely works with JFBConnect. We in no way state you should disable caching for normal operation. The only caching that cannot be used is browser caching, and that's for login functionality (in general for Joomla) to function properly.
Thanks,
Alex