It's getting very hard to live in great cities like SF and NYC on a middle class income. People waste hundreds of hours a year commuting.
Most computers are pwned most of the time. Anything you connect to the internet can be read by determined bad actors.
Burning fossil fuels will probably cause a climate disaster that will put great cities underwater and create food shortages.
Chemicals in our environment are subtly affecting human brains, and catastrophically affecting certain animals like bees and frogs.
Most items in your grocery store are bad for you.
Politics is getting more extreme and divisive. Few politicians even talk about what policies would be best for the people.
One might have thought that everyone having access to all the world's information through pocket supercomputers would make the world smarter. But clickbait journalism, advertising and gamification are filling people's minds with crap and destroying their ability to focus.
Solving 1% of any of these would be a great achievement.
How do we deal with waste in general?
Antibiotic resistance, antibiotics are losing their effectiveness.
Information overload, how can we sort the gems from a pile of coal - metaphorically speaking.
100 years from now, no one will be able to read digital data without its original physical format being available. How difficult is it to read a floppy drive now?
Ditto for encrypted data, everyone wants to encrypt their data now but what happens when historians want to understand our current times?
Replacement for petroleum, it's limited yet it's used all over the place in society.
There's so many more but that's enough for now.
Access to clean, safe drinking water -- including purifying non-potable water at a variety of scales; and delivery, storage; +1 for overpopulated, or money-poor, or resource-poor, or remote areas.
Access to proper sanitation, including safely handling and treating sewage, much like the point above.
Both of these are unsolved in many places that have cell phones, electricity, refrigeration. While it may seem paradoxical, those comforts were easier to solve than water and sewage.
HakuOS is a BEOS clone.
AROS is and AmigaOS clone.
OSFree is an OS/2 clone.
Nobody has solved how to make a free or open source operating system that uses apps and drivers from the original.
Having FOSS alternatives to those OSes is just as important that *BSD Unix, Linux, and MacOS are alternatives to Unix that can run Unix apps due to the API.
There are always problems to be solved like getting everyone solar panels on their house to fight climate change and cut down on their electric bill.
Ask SpaceX why one of their rockets blew up recently. Someone needs to solve that problem too.