I had heard some rumors that an app for the iPhone was under development, but I did not expect to see it until the end of the year. However, this thread on FlyerTalk mentioned that the app had been quietly released to the App Store. Looking back, it appears that Hyatt released the app on October 31st.
A look at the newly released Hyatt Gold Passport iPhone app.
As you can see, the app has five main areas, and then an option to view all of your reservations. I've only used it for a few minutes, but it seems pretty stable, especially since it's built by Hyatt, who is known for having an unreliable website. I plan on booking my next reservation through the app and will update on my experiences with that part of the app, as well as any issues that may show up over the next couple of weeks.