I'm sure I could make a list of a hundred Big Problems without working too hard, many of which have already been mentioned above. And they're all interconnected, to some extent causing and being caused by each other, so it's really hard to find root causes. I've given this enough thought that if I had more drive and organization in my life, I would actually write a book about it.
My own take is that the most important strand in the web is the way capitalism has gotten dangerously out of whack. I genuinely believe that free markets are second only to scientific thought as the greatest historical force for the betterment of mankind, but the system we have today certainly seems to refute that proposition -- global corporate capitalism as it now exists is the greatest force for the debasement and destruction of mankind, beating out even coercive religion. Today, most of the important decisions in the world are made by a tiny group of people on the basis of only one criterion: what maximizes their own corporation's stock price in the next reporting period. It's a serious distortion of the idea of free markets and entrepreneurial capitalism. Corporations are far too big, so that the people at the top are too distant from the day to day effects on individual people's lives of their decisions (whether the people are customers, employees, or residents of communities where the corp operates). And corporations are far, far too focused on the very short term; even a company concerned with absolutely nothing but maximizing shareholder value would be much better for the world if they were maximizing that value in the long term. In the long term, keeping your customers, employees, and neighbors happy is good for business; it's just in the very short run, where the immediate monetary benefits of screwing them are in the time horizon and the long term damage is not, that it makes sense to be so evil.
The screwed up corporations are major immediate causes of most of the other big problems. All our environmental problems from global warming on down flow from the fact that being responsible costs money in the short run and only brings benefits in the long term. The debasement of our media is caused in large part by the fact that most of our media have become divisions of megacorporations, required like all the other divisions to show increasing profits, and real journalism is expensive compared to infotainment fluff. The insane alliance between the environment-destroying corporatists and the intellect-destroying religious whackjobs that is today's Republican party works because the corporate side is willing to work with anyone who helps them achieve their short term goals and is willing to say anything to secure their help, because honesty is another thing that costs extra in the short term and only brings rewards in the long term. Our political system is so corrupt because it's become all about money, a situation that those who have the money do everything they can to protect and enhance the influence of money -- and where's the money? In the corporations.