Very cool news! I had been wondering when this app would come out, and I'm happy to see that it has. So far, the app seems pretty good. For a start, at least. While the various ZAM-related sites provide more information currently than the app, I'm sure it'll be updated and improved. I look forward to seeing how it changes as time goes by.
One of the nice things it does is it allows you to log into your account and view your character data, which is nice. I hope I'm right about this, but it looks like you STAY logged in even after closing the app entirely or turning your iDevice on and off. This includes those, like me, who use a security token. It probably uses the login information to give the app permission to access your account without having to actually login each and every time. You do have the option of manually logging out, of course. Obviously, I do not know yet if it eventually logs you out anyway, but assuming it doesn't, not having to login each time is a huge plus for me so that I don't have to carry my token around everywhere, which I don't like doing. If I notice anything different or find out anything different, I'll edit my post.
Last, it's able to open the security token app for you if you ever need to for some reason (I use a physical token myself).
Primary World: Hyperion
Free Company: Jormungandr
Main Character: Fialas Dawnren: Level 60 BRD/AST/MNK/DoL, Level 16-50 On Everything Else