Still going on our site, just logged in with a test account and also seen a student online. Try these steps to make sure all is OK...
- check no-one has enabled co-branding as this interfered with my login flow (not sure if the bug was fixed but haven't wanted to try and find out!)
- check that your AppID is still correct and alive
- create a new account on Live@Edu and Moodle and see if that signs in correctly
I know MS are doing upgrades on the infrastructure at the moment so it's possible it may have broke something, it's happened before with similar errors to what you're experiencing :(