My staff and I use Office Live because our internal Sharepoint server is up and down.  We share documents and notes.  What I want to know is there a way to get notification if a document has been updated or a new note has been posted?

Unfortunately no. Today, the only way to get those notifications is to actually log in the service and check the activity pane to see if documents have been changes. Nonetheless, we are working to support this in the upcoming releases in a seamless manner.

You will receive one notification email for these actions per workspace after which you need to login to Workspace. The reasoning is that we do not want to flood people with notifications if they are not interested in the changes.

After you login currently we wait for additional 24 hours before sending new notifications, but we're working to remove this filter so the behavior should better fit your needs.