When creating a new portal, DNN threw an error I'd never seen before, something having to do with a foreign key constraint in one of the core tables. So off I go looking into whatever foreign keys might be in place on the Portals table. Nothing to see there, so next stop was to the DNN Event Log. Notice the reference to the invalid object name "DMX_Extensions"
Which led to the discovery of some triggers that had been left behind after a DMX uninstall.
It's interesting to me that without both the error thrown to the screen (which wasn't present in the logs) and the error thrown to the logs (which wasn't presented on screen), the issue would have been more difficult to solve. And say that these issues were being reported by two different people - one front-facing the site (site visitor sees the screen message) and one back-facing (site admin sees the log entry) - it could conceivably be considered as two separate events.
And notice that the key link is the time or time stamp of the event. Just as it is the thing that links these two seeminly disparate error notifications together, it also is the link to other logs on other servers. With it you can take a quick nose dive into the IIS logs to examine details of the exact request and response from the web server. Or to the Windows application and event logs for a view of the event from a slightly different perspective.