It would be nice to have an app (I saw a feature request for this already), but to go along with the app, notifications when share prices go up or down would be nice as well. Otherwise you have to keep checking the site to know if your investment is tanking or doing well. Email notifications would work too.
I'm against PredictIt spending time developing a notification system. The top priority should really be on getting a public API up and running so that third-party devs can build and release their own solutions. A PredictIt-owned app is kind of a waste of time too... just let us build our own please :)