In the calendar view, have a configuration setting to limit the number of days a user can see.
Say you want to only show the incidents for just the past month in the calendar view. Would be nice to have a configuration in admin that says show X days of history. Then if someone views the dashboard they only can scroll back for the X days in the widget. It doesn't necessarily have to effect the search feature for incidents. You could also have another feature that limits that or just allow the search to work for all items.
The first iteration of this feature has been released. The new feature allows turning off event search, and calendar navigation.