Facebook LIKE on articles not working

Ryan,
You get the option to see Admin Page and Insights because you are the owner of the application. Therefore, Facebook recognizes that you are logged into Facebook and gives you some extra options to learn how that Like button is used. It's perfectly normal, and only you would see that. It's possible that the all.js is causing the problem. It's also possible that if you've clicked Like/Unlike 100 times, Facebook has flagged your account as being spammy on that page (though it shouldn't because you're the admin). There's a lot of possible weird things, and I'd really just say, wait it out till it goes live.

The double all.js would be from something installed in Joomla. You can have as many Facebook apps as you want, and they won't insert extra stuff on your page, so that's not the problem. From looking at your page, I'd guess the all.js is included from one of the following 2 extensions:
1) JomSocial - Make sure the Facebook Connect config section has no api/secret key
2) sh404SEF - Not sure why they do social stuff at all, but turn off their integration which they recently added

Hope that helps,
Alex