The value of the dollar is falling because the US Treasury continues to print paper money without anything to back the dollar. The current economy of the US has made investment a risky business for most people. We also continue to borrow money form other countries to back our "stimulus" plans.
The dollar is falling and according to some it may continue to fall, because there is so much of it. It really is a matter of supply and demand. So, if the government keeps printing money, and they printed a whole lot so far, the dollar will continue to fall. The inevitable outcome will be inflation. This is why so many people are trying to get commodities such as oil and gold to hedge against the dollar. So, to answer your second question, I think it is the bad US economy that is driving down the dollar. Let's hope that things change soon.
I would say the lack of strength in the dollar is due to the economic challenges being faced in the States as well as foreign perception about its economy. Foreign perception of economies of scale is very important and part of this confidence is seen in how much the dollar is valued by other countries. Part of this perception has to do with the belief or confidence in whether the United States can finance and pay off its large debt. Foreign nations are willing to help substantiate and lend against this debt. When the dollar falls, it is these nations' perception that this debt might not be able to be paid off. Hence, in the oddest of ways, the falling of the dollar might actually help the United States economy because it will decrease the dependence on foreign debt and help establish some level of long term independence.
Well, it's hard to separate the problems in the US economy from the problems in the world economy. But if I had to pick one of those, I would say the dollar is falling more because of the problems of the US economy than of the world economy.
Mainly, I think that the dollar is falling because fewer people want to buy US securities because they no longer seem to be such a good investment. This reduces demand for the dollar.
I also think that it has something to do with the loose monetary policy the US is pursuing at this time. The interest rate is very low, which also makes US securities less attractive.
At the same time, you should note that the dollar is actually up against the yen and flat against Chinese currency.