Mountain Lion Notification Center is broken

Notification Center in OS X Mountain Lion on the Apple Mac is a great idea: Whenever important events occur you are notified on the screen and messages are stored in the Notification Center, which slides in the from the right side of the screen. It works well for Apple services, but for anything else it is very temperamental and if the wind's blowing in the right direction and you cross your fingers, you may just see a notification, or perhaps not. It seems that Notification Center is broken.

When Mountain Lion was installed I added my Google Mail account to the Mail App, set up notifications for everything, went to the website and logged in so Safari stored the password and so on. The first day, possibly two, I can't remember now, Google Mail notifications appeared in the notifications panel. Since then there has been nothing. There are emails in the notification panel that are over 100 days old. They just seem stuck and there hasn't been an update for months.

Facebook integration was added to Mountain Lion after the launch as an update and this has also proved troublesome. There are currently two Facebook items in my notifications panel, one is four days old and the other is 10 days old. I don't think I've ever seen anything from Twitter in there.

I've deleted all the notifications in the panel (items were days, weeks or even moths old) and it is currently empty. Whether it will ever get anything new is anyone's guess. I'll just have to wait and see.

The one glimmer of hope is that Calendar notifications work fine.