When I check off an item in Today view, the item gets moved out of the view. Sometimes, I check off an item by mistake. Then, I have to switch to another box and get it back. Also, I just want to have an idea of what tasks I have completed today as it is a great motivator to see what I have been able to achieve.

In project views, the completed items are visible, but collapsed by default. I would suggest that they should be expanded by default and be populated with items as I complete them.