I just saw this issue is also mentioned in the thread "Task still showing in “Today” even when the due date is changed" by TahoeJoe. Mentioning my thoughts on the matter here just like in the other thread:
I think it would be best if this section was just an overview of actions / projects of 3 different types:
-actions / projects that were dragged manually to this list in the 'Today' overview;
-actions / projects with due dates today under the 'Today' overview;
-actions / projects with due dates in the past under the 'Past Day's Actions' overview.
If the system would automatically update the lists based on any changes to these parameters that would make it most useful in my view.