Arkham Companion - Features
Load/Delete/Name Previous Games - This allows you to load up earlier games, see their history, continue playing them, etc.
Share History - Like the share option on your camera. E-mail them to yourself or others. Let's you keep a history of what happened in a game
Sync Games between phones - Playing a game with someone else that has a phone? Sync 'em so you can use both phones at once
Mythos Deck - Add the mythos deck and all the bells an whistles that would make it work smoothly.
Additonal Expansion Options - Things like "Only include the OW cards and not the Neighborhood cards"
Support Custom Content - Why just have official expansion? Add support for importing custom expansions
Support Other Languages - (Speaks for itself)
Exhibit and Cult Encounters decks - Add the mini encounter decks from the expansions
Support King in Yellow Touring Performance - Support the optional KiY deck arrangement (Probably would show up in Additional Expansion Options)