The problem: Your Android phone's stock Messaging application says there is one unread message, even though all the messages in your SMS inbox have already been read.
The solution: Install AVG Memory & Cache Cleaner from AVG Mobile. Open the app, go to Calls & Messages, tick the Received (unread) checkbox under Text messages and press the Clean button. Tap OK when it tells you that your device is looking cleaner.
When you go to back to your Messaging application, the phantom notice will already be gone.