Like not so many I use OS X Server (for 10.9) to cache Mac and iOS files, serve backup files and to serve PHP for testing locally. I recently discovered a quick trick to clear a push notification. I use multiple machines to manage the server and one client was stuck with two recent notifications.

To clear stuck Alert notifications from the dock:

1) Verify all notifications have been cleared.

Here is an image, hit the gear icon to clear the notifications. 

2) Still stuck push notifications in the dock?

After hitting clear, switch to the deliver tab up top. Now using the same gear icon you can "Send Test Alert" which should send an extra alert, but clearing this alert will clear the stuck Alert.

 

Notes on my setup

As an aside to the OS X Server package is not the simplest system to restore from backup. Apple does give this doc: http://support.apple.com/kb/ht5139 but I decided to virtualize the entire server using VMware Fusion. This allows me to reboot the VM daily but keep my local machine online constantly. I also created a small app to use the VMrun command to issue suspend and start commands to my machine.