When I subscribed I tried the iPad app before the iPhone app... didn't work.
Oh well, I guess I can live with the slightly pixelated video. Here's hoping MLB decide to let us watch on the iPad using the mobile subscription.
--EDIT
I seem to have got the mobile subscription to work with the iPad, at least for now.
I deleted the (native) app from my iPad, rebooted, then reinstalled it. Then when I opened it I went to settings and cleared my MLB.tv account details using the button at the bottom. I then closed the app and completely killed it from the multitasking bar. Then I opened it again, entered my MLB.tv details, and it works! At least with archived games, will have to try it with a live game later today.
It's possible that all you have to do is clear your MLB.tv details from the settings page and that will do the trick. However, I thought I would post the full procedure I went through just in case.
Archived games have always worked on the iPad, the above method does not work for live games using the iPad app. The only option is to use the iPhone app on the iPad and deal with the slightly pixelated video. I probably wouldn't have bought this had I been aware of this limitation.