Omnifocus does this beautifully. For all projects, it shows due soon and overdue task count in the sidebar. So without going into all projects, you can get an idea of overdue tasks. Red is overdue count and Amber is due soon task count.

Comes in very handy when you are switching contexts. For example, at a glance you will know that Home, work and person projects have some overdue tasks and can plan your day accordingly. Please see screenshot for details