Worlds Biggest Problems

1. Water Scarcity. Some have predicted we may very well see "Water Wars" in our lifetimes. This isn't a problem unique to the poorer areas of the planet. Over the summer we saw these problems take shape here in our own country in California. This is a complex problem with many causes, overpopulation being front and center. My suggestion would be for municipal governments in at-risk areas to take a more active role in managing water supplies, and ensuring agricultural consumers are not abusing the public supply.
2. Finite Energy Sources. While we are currently enjoying gas prices we haven't seen in a decade, it will not last forever. Eventually the wells will dry up, and when that day comes we had better have a proper infrastructure built to supply our energy needs. My suggestion would be to open up the fuel market to ethanol, methanol, and CNG in the near term, and expand investment in electric and hydrogen propulsion for the future.
3. Poverty. Poverty is a problem that has plagued man since the dawn of civilization. It has to many causes to list and has led to war and revolution around the globe. My only suggestion would be for international organizations to focus on ensuring people have access to education and a free market. 
4. Apathetic, distracted populations. Democracy fails when people stop paying attention and become complacent. This allows individuals who do not have the interests of their people at heart rise to power. Returning civics education to our schools would be a start, but the best answer would be to foster an environment where citizenship is prized not just for its handouts but also its responsibilities. 
5. ISIS/ International Terrorism. Terrorism represents a threat to civilization, both west and east. As the late Jeff Cooper said "The only answer to violence is more violence, applied by the right people in the right way. A true international coallition must be formed to meet this threat. Not one based on alliances from the Cold War, but one that brings together the West and the East together in common cause.
6. Corruption. Governments are supposed to be the voice of and advocate for the people. To fight corruption the laws must change to view the betrayal of the public trust in this manner as the heinous crime that it is. One corrupt individual undermines the entire system of government, especially when the perpetrator is given nothing more than a slap on the wrist. 
7. Waste. No society can ever achieve 100% efficiency, but we can certainly try harder than we are now. When living on a planet with finite resources we should take better care of what we have. We are now seeing the effects of previous generations' mishandling of resources, and if we want to have anything to pass on to our decendants than we must understand that that will entail sacrifice. 
8. Social division. Society seems more divided now than ever before. If we do not learn to put aside our differences soon it is highly likely we wont have a society any more. Difference of opinion will never go away, but what is most important is that we restore a sense of national identity. Once we can all agree that we are at least on the same team perhaps then we can more forward. 
9. Greed. Greed is seen in every class of society, from the top 1% to the bottom of the ladder. Some would argue that greed is a part of human nature, an extension of our survival instinct. The only solution, if you can call it that, is for society as whole to understand that fulfillment doesn't come from having the most stuff. 
10. Suicidal altruism. Our western liberal values and Christian traditions have taught us that we must provide help to those in need. These values certainly aren't wrong, but they must be measured against the cost. No society can withstand an unlimited constant influx of unassimilated foreigners. For us to help the world first we must ensure our own people are safe and secure.