For the Emerging Markets category, consider that there are people for whom a mobile device is the closest thing to a PC for miles, and cellular data is the only digital connection to a larger world. While multiple vendors are trying to make the $100 laptop PC to serve emerging markets, mountains of refurbished and donated Series 60 devices are ready to distribute for the cost of transportation. Even long-discontinued devices are surprisingly capable computers. Consider accessibility as an emerging market as well. Many Nokia devices have integrated speech synthesis and recognition. Finally, you might look at services or applications that are supplied in a limited number of languages and internationalize them.
For the Eco-Challenge, I suggest considering Nokia devices' prowess as radio transceivers. The cost of equipping environmental sensors (including current sensors for power monitoring) with Bluetooth, Wi-Fi, infrared, or even GSM signaling is dropping fast, and Series 60 native code can process, log, and respond to sensor input with minimal lag. Nokia devices are loaded with sensors of their own. Depending on what you want to measure, the cheapest sensor may be the Series 60 device itself.
My point is less about Calling All Innovators than it is about seeing mobile devices from top-tier manufacturers, with open and well-documented APIs, for what they are. They are mobile computers, capable of things you'd never dream of asking a smart phone to do. Someone once imagined running a Web server in the background on a Nokia device, and someone else wondered what it would be like to drive a handset's display and keyboard remotely. Both of these stereotype-busting applications exist. Take them as inspiration and run with it.