This is what my inbox looks like:
When I opened it today it had a red (3) and a blue (1). The notifications list is working, but I only see one out of three inbox entries.
And this is what I see when I visit my network account (to check my full inbox):
This seems to be happening to a lot of users (eg this guy, chem account).
Looks like SE.com (which IIRC provides the inbox as well) is down :/