"Select Banner" button is not working

I don’t know if that button works differently from regular WP or Multisite…
I would assume it’s the exact same procedure and libraries. Does anything show up in the browser debug console when you load the page or when you click the button?

I don’t develop on Multisite so anything you try in there is untested and unsupported.

Ok, in Firebug I get the following when loading the ad management page:

Blocked loading mixed active content “https://mysite.com/wp-content/plugins/adrotate/library/uploader-hook.js?ver=3.6.1”

I run the admin over HTTPS, and the content above is loading over HTTP. This is a security feature with Firefox 23+.

Ah, so your site runs on https?

Just the admin panel. But, the configured site URL is non-SSL, and using fully qualified URLs will result in such an error in Firefox with that security protection enabled.

I’ve checked the code. AdRotate uses WordPress functions to build that url. If WordPress does it wrong for your situation that’s beyond my control.