Mark Z. decides to prove the positive benefit of using his platform, so he invites 1000+ volunteers with varying skills, resources, locations, etc to swarm around ideas and get stuff done that is a combination of cool, fun, and interesting. It could be online, IRL, or a combination.
You get randomly selected to submit the first project idea to the group. What would you have them do?
Essentially I'd take the old 20% Friday idea from Google, and make it 100%, I'd take point on managing the herd of cats that results, until I found someone way better at it.
Personally, I'd try to run down every hint of over-unity in energy production I could find, like cold fusion, cavitation as an energy source, etc. I'd systematically make sure that none of them work within experimental bounds, and publish all the results.
My current personal project inverts the web, which in practical form is a challenging concept to communicate. The benefits of the idea are numerous and obvious but only in hindsight.
I would go broke since I dont have money to pay them.
Beneficial software projects could be good. Stuff like making charity or government services more accessible. If you have that much money, then you probably have a platform and connections. Maybe try to clean up bad laws, policies, etc by taking requests for help from the people affected.