A PADD app for tablets (Android, iPad) that let us log in and do certain trivial things, like read/write mail and manage duty officer missions, would really be outstanding. (It'd be particularly awesome if we could log into it at the same time as the full game client, using a PADD as a captain in Trek really would.)

I'd love that too! And I know that the Devs would like to integrate it as well!
It would be pretty cool to check the Reports of your DOFFs and send them on new assignments.
Hounestly, did anyone read the reports of a DOFF mission? I might do it on a PADD but ingame I just click to get the reward.
I really love the DOFF system and this would be a greate addition to the game!!

I was just thinking about that. I'd love something like that on my Galaxy Tab.

Eve has an app that lets you manage training a doff management app should not be a problem. Even a doff management on this website would be cool.

I think it gets down to license, as in they may not have the actual license ability to do that. SO if that's the case it doesn't matter how easy or nice or cool or whatever it is. If the license doesn't allow it, it won't happen.

What you can do is to get a remote desktop application such as jumi one, then you can doff away at your leisure on your PADD