Can you please enable dev mode and refresh the website, then disable it again?
If the issue persists
Check your firebug console for any javascript errors while uploading the image.
Given URL is not allowed by the Application configuration.: One or more of the given URLs is not allowed by the App's settings. It must match the Website URL or Canvas URL, or the domain must be a subdomain of one of the App's domains.
Check your error logs as well.
If you see any error in error log or after enabling debug mode paste the error here, as we could not reproduce the issue and you don't give details to your website.
Changing avatar is avatar/core functional.
I recommend you to restore your back up and try to do the update again as we do not have access to your website and server and I can't help you much with this.
probably some files are missing or have not been overwritten, probably the database has not been updated.
As I noted earlier, we cannot reproduce any of the reported issues regarding avatars/changing avatars, photos etc. These are issue are individual and are only on your website. And I can't say what exactly is wrong until I look at the code and database.
Harry