Some medium-sized unsolved problems:
- Solar panel installation. Installation is about half the cost of an installed system. Figure out how to get that down. Can solar panels be integrated into roof systems? And last for 40 years without leaks?
- Police paperwork. Cops spend far too much time doing paperwork, which they hate. There's pressure for cops to wear body cameras, which they also hate. So come up with a system where the body camera images, audio, GPS info, and what you can pull from police files are used to put together most of the arrest report. Cops would like that. Start with something where a camera glance at an ID or license plate or face fills in much of the details.
- Tablet based basic education - reading, writing, spelling, and basic arithmetic. Not just canned lessons, ones that adjust adaptively to the student's performance and errors. Ship on a $50 tablet.
- Good $50 tablets. Some are good, some suck, some have weak points. Evaluate some, find the weak points, talk to the manufacturers in Shentzen about getting them fixed, and set up a distribution chain where they're sold in bubble packs in the back-to-school section of stores.
- A rugged phone with no holes in it. No connectors, wireless charging only. Permanent battery. Hermetically sealed at the factory.
- Intelligent HVAC for homes. The next step after "Nest", which can only turn heat and A/C on and off. Window fans and A/C with inside and outside temp, humidity, CO, and CO2 sensors. Outside air is used as much as possible. The whole system learns the house, self-adjusts, and doesn't need HVAC engineering.
- Video from talks where the speaker image and slides are combined intelligently, with the system deciding when to emphasize what.
- A PA system which absolutely cannot feedback. It's a simple DSP problem; why isn't it everywhere?
Those are a few ideas to get you started.