Currently the ipad and iphone apps show past due items in the Today list. This is inconsistent with the Web version which shows past dues as a separate list from Today.
I think it would be much better to have a user defined switch which would allow the choice to include or exclude past dues in the Today view.

I know this can be approximated via a Smart List, but the user interface on the ipad/iphone is easier to use with just the built in lists.