Some scripts don't work anymore when served from the CDN

In those cases, it is best to simply make CDN for Joomla! ignore those files.

For instance, Facebook scripts often break when they are not run from the website itself. So if the script name is facebook.js, just place facebook.js in the Ignore Files field.

How do I set up CDN for Joomla! to work with Amazon CloudFront

Please see the full tutorial for that here:
How to use Amazon CloudFront in Joomla!

How can I keep using @font-face styles when using a CDN?

Try adding this to your .htaccess file:

<FilesMatch "\.(ttf|ttc|otf|eot|woff)$">
<IfModule mod_headers.c>
Header set Access-Control-Allow-Origin "*"

If that doesn't work, you can make CDN for Joomla! ignore your @fontface css files.

Place all your @font-face declarations in a separate css file called font.css.

Then just place font.css in the Ignore Files field.

Now the font.css file will be served from your own website instead of the CDN server.