My phone alerts me that I have a new message in my Stack Overflow inbox. After I read the new message in the Android app it shows 0 unread messages. The next time I visit the main site on my notebook the new (December 2013) Top Bar says that I have one unread message: the message that I read on my phone. Even if I shut down my browser and wait a few minutes (to give the Android app time to "sync", or whatever), the new message indicator in the new Top Bar doesn't go away until I click it.
I don't recall this happening with the older top bar, so perhaps the new Top Bar and the Android app need to get better acquainted.