Ever see the notification on your Messages app, but have no luck finding it? Use Siri. Activate Siri, and then say "Read me my unread messages". Siri should then locate and read the unread message, after which the notification will go away.
I had a user that this happened to today. The odd thing was the message in question had been read and deleted already, but somehow hadn't been marked read so the notification kept coming back no matter how many times the user went into that particular message thread. Using Siri took care of it.