Does this happen repeatably? This doesn't appear to be a Linux issue as looking for "stuck notification" in the Steam forums turns up a number of very similar comments in Windows steam. Pursuing the issue through those forums would be the best way to go forward.
If this keeps happening one suggestion was that in your Comment Notifications page there's a "Mark all as read" button that you can use to clear the notification counter, avoiding a restart.
I saw this happen once, have not gotten another notification to see if this is persistent. It may just be a wild goose chase.
OK, I'm going to close this for now.
Nothing extracted yet.
I was notified that I had received a new comment on a Steam forum post I made, but after viewing the message by clicking on the notification that linked me to the post, the notification symbol still displayed that I had a new notification (that was in fact the same one I just visited). After clicking on the notification multiple times and waiting 10 minutes, I restarted Steam and this seemed to fix the problem.
My Help -> System Info:
http://paste.ubuntu.com/5565385/