Boil down all the worlds problems? While it seems to be a very complex question, the answer is really quite simple. The answer is that despite all the good we want to do, human beings are not perfect. We try to do what might be best for everyone, but when all is said and done, we all will do what is good for ourselves.
Think about all the good things that people do, and why we do them. We give to charities, and sure its a good thing to do, but think of the efforts that the charities have to go through. If the Salvation Army wasn't standing right outside of the mall, would we give to them? If we didn't get countless fliers, phone calls and other notifications would we be as willing to voluntarily give money to an organization.
Why do we only give to countries like Myanmar and Indonesia when cyclones hit? Aren't these countries in need pretty much year round? It would be nice if it didn't take a media blitz to get people to open up to the rest of the world. Granted I have yet to donate to these countries either, but that would take two things: First, money available for donation by me, and two, the fact that Myanmar didn't even allow much of the aid in that foreigners gave.
This brings me to my next point which is that humans are selfish, and prideful. Myanmar didn't want foreign aid because it didn't want to lose its grip on power. So instead of helping its people and at least establishing some sort of legitimacy, they became a junta that killed its own population. Its the same reason Hugo Chavez is in power in Venezuela. He claims to be for the people, yet he only truly wants to have unlimited power for himself and his friends.
Terrorism could almost be eliminated singlehandedly by eliminating the human emotion of being selfish. First even if terrorism did exist, we would be more willing to negotiate to eliminate the grievances that the terrorists have. On the other hand, terrorists would have no need to terrorize if they were truly looking out for the good of fellow man. Honestly, would someone blow themselves up, or have someone else blow themselves up for a cause that would seem horrifying if not forced upon the masses by a rogue terrorist regime? In other words, its either support the terrorists, and the money they provide, or live in fear of dying in an attack.
Hunger and war could be eliminated too. People would be willing to give what they had, and people would cooperate to do things like produce food, and figure out ways to make it last longer. Sure, we had communism, but that failed because in the end it too was only beneficial to a few in power. If there were fewer conflicts over resources, we could eliminate the need to go to war, and kill needlessly to settle issues, again, that only help a few people in power.
We probably would have a robust space program, and asteroid defense shields up too if we cooperated. If all the nations of the world had equal access to information, and felt motivated to find and share new data, we could be light years ahead of what we currently know. Sure this doesn't rank up there as a huge problem, but if an asteroid were to hit, I blame the shortsightedness of humanity!
Sure, eliminating the problems of the world would probably lead to new problems. Read "The Giver" if you want an easy to read book that explains what I am talking about. Our humanity is what makes us special, but it is also to blame for why the world is so messed up.