Very nice, I was hoping there would be a simple checklist like this soon (certainly beats using Notes for shopping).

I have a few suggestions though:

1) The arrows in the viewheader indicate a filter, viewheaders should not be used for menus (as in Fremantle), since there is a menu button in the lower right. Instead, I suggest that tapping the view header opens the list selection. Also, please show the name of the list in the viewheader, as I would find this far more useful than the application name.

2) This is minor, but I find the use of the term "selected" somewhat confusing. It made me wonder at first if there was a different way of selecting items, rather than checking/completing them. I would suggest "checked" instead.

3) The way you handle multiple lists is somewhat clever, but I find it terribly confusing. The only use case that is straight forward with it is the one of cloning lists, which I never need. On the other hand, the common tasks of creating a new blank list or renaming an existing list require multiple steps and are really not very intuitive.

I would suggest to just use the standard method used by other applications in Harmattan: A "+" button in the toolbar to add a new list, and rename (or delete) items via the context menu (long press on item). The input field can then be removed, and instead appear in a sheet when a list is added or renamed. It may seem crude, but I really think it's good enough and nothing fancy is needed.

Another advantage of doing it like this would be that you could switch immediately back to the list view when a list is selected. To delete multiple items, you can still keep the delete button in the task bar and make it work like the delete function in Contacts for example (it opens a sheet with a multiple selection list and Cancel/Delete buttons at the top).

I also do not like that lists just disappear, when they become empty.