So far our awesome Destiny app tells us almost everything we could need to know, from game stats to reply notifications (although that is broken right now)
What we need for the app to send us a notification ping for imminent special events such as iron banner and similar
Would you find this handy or just an extra annoying ping on top of skype, fb, twitter, email, family guy the quest for stuff and for everybody from 1998, myspace
EDIT
Addition from Mrketch. Ability to see guardian without helmet in app
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I would also like to see a section to see your current rep standing with the different factions.