I've been using the iOS app for a few years now and really disappointed with the lack of new features. I would love to have these features added since I rarely come to the site and the app is my main source of consumption:
7-15 second skip and rewind
Expand show info in the app to show genre & simulcast info
View show comments
Add the license end date to see when a show is going away or add some sort of indicator (!!) that is going away soon (You can show a warning in the app letting me know that Plastic Memories isn't available in Italy but you can't show a warning that a license is ending soon?)
Create or at least manage groups completed vs. in-progress shows in my queue
Notifications to be push notifications when a new show is added (currently I get an email days later)
I don't know what the other mobile apps are like but any of these would be helpful.