I also use email notifications, but I also have all of these messages in the database table with a flag if it is related to data import, wrong password, etc.
Users, when notified or not, can see this log (or timeline) in the same way that Trac (bug tracking software) or Facebook displays news. This is a feed that you can filter by various criteria.
Some people may be interested in messages or errors related to data import, as well as authentication problems, etc.
Another thing is you can send these notifications by e-mail or do more "broadcasters" such as Jabber / XMPP messages, twitter messages that your users like.
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