This bug was solved on 12th oct. It is possible that you haven't logged out since that day & it is showing because of issue.
Please logout & clear your cache & cookies.
Than login again.
Also try incoginto mode for chrome & if the bug still exists. Submit a ticket here
http://support.plarium.com/enpirates/Tickets/Submit/Step1/53
it appears its just the msgs from a certain point as i can now get msgs but i cant see the 4 from the time it was bugged.........as for a bug report i think i will just have to deal with the problem along with the other glitches
.........i will try directly logging out tho as i had already tryed clearing cache and cookies
(edit)is there a log out button if not then i have loged out already when i leave the game havent i ???)
For logging out click on your name in top right corner, it will take you to your profile in a new window.
Scroll down & on bottom left you will see logout.
Additionally i believe you haven't any unread messages it is just the bug which is showing 4 unread.
Additionally you can try incoginto mode , press Ctrl+Shift+N for chrome