George Nguguna is developing a mobile phone app as part of his MIT course in Java/J2ME to enable people to easily contact institutions by providing their contact details. The free app will have integrated advertisements while a paid version will not have ads. It will start by including contacts for key institutions but George plans to add more functionalities and institutions over time. Some challenges to completing the app include high expenses, a time limit for the course, frequent power failures, and potential coding errors.