The Mac App in many cases looses focus, that is, keyboard input is not recognised anymore in various situations. Keyboard input is essential for speed and a good user experience, so I hope you prioritize to look at this.

When switching focus area:
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When going from one focus area to another (apple-1, apple-2 shortcut keys etc), pressing up and down arrow keys no longer lets you traverse the list items. You need to click with the mouse first.

When switching to another app:
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Regardless of where you had focus and input before, after switching to another app and back to doit.im, you no longer have input (exception is the edit dialog, which retains focus). So if you for instance click a task, move up and down with arrow keys in the list of tasks, then cmd-tab to another app and back again, you no longer have focus and need to click again to be able to use the keyboard.

When saving a task:
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When saving a task (after editing it), you are no longer able to navigate the list with the keyboard as you were before.

If you start by traversing the list of items (by clicking on one item and then using arrow keys to move up and down) you can start editing with enter, and exit with esc and not save, and then continue traversing the list. If you, however, edit this and save it with apple-s, the list does not have focus and all you hear is the default alarm sound from os x if you press any arrowkeys. You now need to click in the list with the mouse to retain focus.

Quick add and return-fields:
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The quick add field on top of each focus area cannot be moved into and out of (that I have found at least) on the mac.app. This means it isnt really quick input...! This should have a separate key command, e.g. shift-Enter or apple-Enter, to get focus. Esc should move out of it, to have the same escape function as in the edit screen.