I have just run into this issue as well and could not find a way to dismiss or cancel a broadcast notification.
I could not find any entry on the Voices board so I created the following:
http://stackideas.com/voices/easysocial/item/998
If you're here for this feature, please go vote!
Arlex/Stackideas team,
Is there a non-graceful way either via the backend joomla or even the database to dismiss or cancel a broadcast popup or notification for all users? Or is this broadcast sent and stored with each user, requiring admin to edit one user at a time?