synchronise with OS X tasks
Doris tasks would appear updated in Mail.app
Much better to synchronize with Apple Calendar., Many users use something other than Mail for mail, mostly gmail. I never understood why Apple put tasks in Mail instead of fixing Calendar tasks for the iPhone.
yes, and it should work in both directions. A new to'do created in Apple Mail or iCal should show up in Doris, and all doris items should show up in Mail and iCal.
The difficulty, of course, is the different data. How do you deal with due dates, priorities and the "calendar" fields from the Mac's to-dos, (and with Doris' categories) without just ignoring that data. Tricky.