After a comment from MasterAtArms I discovered that the PM popup wasn't working. I've now fixed that problem and you should get a popup message after you receive a PM, if you've got the option enabled.
Additionally, the icon in the stripe at the top has now been slightly modified. If you have no new messages and no unread messages, it'll show the white page icon and say "No new messages". If you have no new messages but some unread messages it'll show a coloured page and say "No new messages" (since the unread messages are now old). Finally, if you have new unread messages it will show the coloured icon and say "X new messages". Also, if you hang over the icon then you should get a tooltop telling you how many unread messages you have.
Hopefully the additional indicator of coloured icons for unread messages should make it a bit clearer as to when you have new PMs