I was experiencing some trouble with SharePoint 2010 alerts. The SMTP relay was already configured and may would send, so we knew the infrastructure piece of this was configured correctly. My work-group was testing various options for alert criteria from the SharePoint end user UI.
In order to see what was actually taking place, I enabled monitoring. This can be accomplished using Central Admin by selecting Monitoring -> Configure Diagnostic Logging -> SharePoint Foundation -> and selecting Alerts. At the bottom of the page, select your Event Log Levels and Trace Log levels.
Now you can start using Event Viewer and the SharePoint logs to diagnose Alert errors.
