Problem 1: Us-vs-Them-ism. Call it tribalism, nationalism, racism, whatever. Any time you divide the world into Us and Them, you're asking for trouble. Unfortunately, that's how we evolved to view the world.
Problem 2: The Expert Syndrome. Any time you find someone who's absolutely convinced you should live your life some other way than what you're doing right now, you've got conflict. Religious zealotry, health-nuts, safety nazis, the list goes on and on. "I know better than you, and you should be forced to do things my way." Both halves of that statement are also how everyone evolved to view the world. The first half (I know better than you) isn't that harmful in and of itself, it's the second half (you should be forced to do things my way) where things fall apart rapidly.
There. I've pretty much identified the basic problems with the world today. Somebody needs to go out and fix them. Actually, everybody needs to go out and fix them.