So many — here are a few large scale problems I think about lately.
* Trustworthiness of content (text and soon photo and video) is and will be a fundamental problem. This is the basic attack vector for national and global politics in the last few years. Anyone with a good solution would help the world immeasurably and have their pick of customers.
* fall out from monetary policy in the us and Europe: take your pick, but for example - home prices in urban areas; figuring out how to house families for 1/2 or 1/3 current prices in the United States would have a lasting impact on stability and wealth creation.
* the continued effectiveness of state propaganda; related to my first suggestion above.
* obesity in the us and soon Western Europe.
* data security - fixing large scale data breaches.
* what I call long range to short range : problems too big for people to think about or accept abound, like climate change. Finding one and figuring out how to tie to short term incentives creating a positive feedback loop would be a real game changer. Oil does this all the time but usually not with good long term consequences - cf fracking turns North Dakota into a boom zone — creativity around good not pernicious cycles would be a boon for the world.