Of course the app is not easily named, nor is it particularly beautiful (both a big surprise I'm sure). It is called "The Official Mobile App of The United Methodist Church General Conference 2012" which meant that the only way for me to find it in the app store easily was to follow a link from the UMC site. Try typing that with your thumbs! However, the app is pretty solid on the whole.
You are able to search for and view individual petitions, read the current news and watch a live stream. That about covers every aspect that I was looking for, but if you are one of the lucky few to have been sleeted to spend 12+ hours a day on the ground a General Conference, it also has some features that will help you navigate the ins and outs including a schedule and a map that can link into the iOS location data to help you get where you need to be.
All in all, I'd say every United Methodist that cares to know what is happening over these next critical days needs to download the General Conference app.