I'm filing this as a candidate sub-issue of the #151 META...
There's the Views Watchdog module for Drupal that does this (could be others too) and we can use that as a starting point. I imagine that the "Top 'access denied' errors" (/admin/reports/access-denied) and the "Top 'page not found' errors" (/admin/reports/page-not-found) report pages can then simply be filtered versions of the same view and on top of that we can expose whichever of these views/displays as blocks that can be then used in #495 to create a (highly customizable may I add) dashboard.
Thoughts?
Recent comments
That would actually be a nice usability improvement. A lot of people already build search pages with Views, so having an easier way to convert the default search results into a View would make...
[UX] Convert search to a view.
Try using caching in the View settings, set to 24 hours. This should work for anonymous site visitors. I haven't tested this in practice, so this is just a guess.
View to show a different node each day
Have you already played with Views random seed? I belief, what you try to achieve would work with that module. Show only one node and set the sort order to "Global: Random seed" with "...
View to show a different node each day