Some big problems easily solvable today
- Create artificial general intelligence
- Create an immortal mice using focused ultrasound technologies (non-invasive surgery and localized drug delivery)
- flying cars (drones) including air traffic control for everyone on earth (+ cargo drones, so 1 trillion air vehicles or more)
(That's in addition to the important prizes already like x tricorder and darpa humanoid)
Up the prize money to $1 billion each (that's nothing compared to the bailouts) and you'll see all of the above done within 1 year, they really aren't difficult if you put a little thought to it. There's more than enough money and the technological pieces are in place. It just requires some bold thinking.
No one holds people to account for opportunity costs. The robocar challenge showed that robocars were possible. Governments and car companies should be held to account to account (sued in court) for not working on it sooner. That delay is millions of deaths. The same is true for other techs as mentioned above. Some economic indicators need to be put in place for tech development that isn't being done (opportunity cost accounting).