Well off the top of my head for starters,
I dedicated spot on my home bar
push notifications
quicker log in
centering page focusing at the right size to be clearly read on the I phone
In app payment via loaded payment info.
The coding could have most of the GUI loaded in the app which would speed up loading time, as well as decrease data usage
And finally it wold be cool!!
Off the top of my head, if they are interested in further ideas they can site mail me, im sure I can think of a lot more.