I've had this problem for two days now. I sent a friend a message on Facebook using the app and something went wrong.
I've tried deleting the message from both my inbox on Facebook as well as my messages on my phone, battery pulling, and uninstalling Facebook and reinstalling.
For the NOTIFICATION icon to disappear usually you need to go to Blackberry's native "Messages", scroll down to the facebook message and follow the link from there. Then the icon disappears from the notification bar.
Reading the message through the facebook app won't solve your issue.
Posted from my CrackBerry at wapforums.crackberry.com
I've tried doing the Mark Prior and that didn't work, and now the message has been deleted from both Facebook, and my messages. I remember seeing the message and it had the lines like it was still trying to send, even though it was sent. I would try to delete it from my messages, but it wouldn't delete. Then when I battery pulled, the message was gone, but the notification icon on the homescreen was still there.