Just to let you know that BA have updated their smartphone app (at least on the iPhone) with the said updates.

It really does look sleek.
Confirmed: It offers book with Avios and upgrade with Avios in the MMB app. Although I thought the new digital membership card will be on Passbook, it is not, but that's the only thing I noticed that wasn't there.

Mods, feel free to merge this into the main BA App thread, too.