Congratulations on Twilight Struggle for iOS (at least the Offline Mode, which is the only one I tried)!
Now, I have a suggestion that would make the play experience more enjoyable for me: being able to display the cards played so far (by tapping on the turn counter) is nice, but it would be even nicer if we knew which cards were played for their event (for instance by using a colored frame for these cards, or a colored title, etc.).
This would allow players to keep in mind the key historical events that define the game, adding add flavor and (for me at least) even more enjoyment of each game.
Anyway, keep up the good work!