See who any Facebook messages are posted to

On Facebook when accessing messages, you can change the message id in the URL and see for any message who it is posted to.

e.g. try this in your Facebook account: https://www.facebook.com/messages/503348860 or see a screenshot here: http://postimage.org/image/a6w7x76yv/

It doesn't show the message so I can't think of a serious problem but I'm not sure I should be able to see who a message was posted to.

That is not message id, it is the profile id of the person to whom message is to be sent.