Hi,
I have a routine.
At about 7pm my time (your first post is timed and close to 4am) I start by looking at email notifications form the Apple Communities and answering new replies to threads I am already in.
Depending on the number and the complexity I then read the Unread items in Mavericks using the iMessages and Messages filter, followed by a similar option in the Mountain Lion areas and the standalone iChat Area.
Around 10pm I finish for the "day".
Your 6.43pm post raised your post back up the list of unreads.
This issue in Mavericks is unclear at the present moment.
Something similar did used to happen in iChat and Messages 7 in Mountain Lion.
Open a Finder window.
Now use the Go Menu whilst holding down the ALT key (The one two away from the sapce bar on either side)
This will show the Library in the menu list. (the Library is hidden normally)
Select this.
No navigate to the Preferences Folder.
Find com.apple.ichat.plist (Messages is built on thre iChat engine)
Drag it to the Trash and relaunch Messages.
The .plist will be recreated
At present this "fix" is not as successful as it used to be.
At this point if it was not successful open Applications then Utilities and Open the Disk Utility item
Change the tab to First Aid if not already selected.
Select the Macintosh HD if that is the drive you are booted from.
Chose Repair Permissions bottom left of the right hand pane.
This may take a while to run.
As I said it is late here and it will be a while before I pick up on further replies.
10:18 pm Friday; March 28, 2014
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