I was a little late jumping on the smartphone bandwagon, so maybe I could be considered a bit of a luddite, but I don't see the point of a "stage management app". Right now what I have is a folder of an assortment of free apps on my phone that work well for stage management. I think a single 'multi-purpose' app would just be too bulky for the variety and scope of work we do. I have a free Microsoft office suite type app, Scan to PDF which turns my photos to PDF files, a Stopwatch, Dropbox, and Box. All of which were free. And work just fine.
(And many apps I have found through recommendations from here- Thanks!)