HI,
IF you click on the DOCK icon does it list the "Unread" iMessage (or other message)
Is it one you have dismissed as you read it on your iPhone.
Try and select it from the DOCK icon.
If it is "Selectable" it will open and you can "read" it again.
If not go to Applications/Utilities and open Activity Monitor.
Scroll down until you find the listing for the DOCK.
Select it and then use the x icon top left.
Confirm Force Quit in the dialogue box that appears.
The DOCK will disappear off the screen until the app that runs the DOCK that you just Quit restarts.
The Unread marker should be gone.

9:00 p.m. Saturday; July 11, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad