Hi Dewi, that's strange that the problem just started as I did some searching on
Mac mountain lion Mail Notifications problem and was going to post that maybe your ISP was correct.
It seems that many had goofy problems with Notifications with OS X 10.5.x when it was first introduced, but that doesn't make much sense if your problem just started.
I don't know what to suggest.
As for your OS X versions, and a suggestion my son told me years ago, and this is where Google can be your friend. His trick was to start the question with
what is… and so doing that with your question, you would enter
what is os x versions and from those hits, you'll get:
OS X - Wikipedia, the free encyclopedia
Finding the OS X version and build information on your Mac - Apple Support
Mac OS X versions (builds) for computers - Apple Support for specific builds
etc. etc.
That method often works well.
I'm not trying to sound glib, but like sort of like teaching one to fish.
So in your case OS X 10.8.x versions are all referred to as Mountain Lion
I hope that helps. I'll keep thinking for possible Notifications fixes, but maybe keep close tabs and notice which Notification you actually click on, as if you haven't been doing so already.
EDIT:
I just thought, at least for a possible fix would be to use
Herald
Available at:
http://www.macupdate.com/app/mac/32744/herald
Might be better than what you've got and overcome the problem.