In ArcGIS Mobile for Windows you could configure searches so the user could say, return a list of all the inspections in a particular status, either in their map extent or for the full extent. This would be great functionality to have in Collector. The search function that you can configure in the web map doesn't let you filter by extent, plus you can only have one field per layer.
Something just like the filter widget in the web map or in web apps is what's needed. In mobile for windows you could even write your own queries, but at minimum I think it's useful if they can be configured for all users.