You have to be an app developer for that to work: /me/threads is accessible only to developers of an app, and there is no permission that you can grant to an app to make it work. Otherwise, you get:

  {
    "error": {
      "message": "(#298) You must be a developer of the application", 
      "type": "OAuthException", 
      "code": 298
    }
  }

You get this even if you try to use the Graph API Explorer tool to view /me/threads.

Do we know if Adium/pidgin are likely to update to use that API, or is it too early to say?

Someone will build it. But it still just adds another proprietary API to the arsenal. Ugh.

I echo other sentiments here: what exactly is broken about XMPP that companies keep moving away?

Somebody already said it: while using the chat through a different client than their web chat, you're not looking at their ads, you're not installing their proprietary mobile app, and so on.

Can you link to the example? I've been interested in doing something like this, but as far as I can tell, you can only read messages using the Graph API; there's no method for sending messages.