Whether this is good or bad in an economic sense is very complicated, and that is not the reason this is causing concern anyway. The reason this is causing concern is WHY the dollar is going down: Apparently, sovereign nations are speculating against the dollar. BTW: This is considered very bad form in diplomatic circles.
Some background may help: The value of a currency will fall during a speculative attack, but if the fall does not become self sustaining, the speculators will lose a lot of money. Speculators are gambling that future events will cause the currency to decline in value on at least a temporarily sustained basis (at least long enough for them to reverse their speculative positions at a profit).
So, the relevant question is WHY sovereign nations would think the value of the dollar is going to go down. The implied message is that they know something that the rest of us do not. And they see enough profit potential to justify committing a diplomatic faux pas.
If dollar drops, then foreign investors are unlikely to maintain their investments in the United States, which are held in dollars.
If these foreign investors decide to stop investing, or to unload the investments that they hold, the impact on the financial markets will be severe. The United States requires $2.7 billion of imported money daily in order to meet its financial needs. If it becomes more difficult to attract this money, then interest rates will have to rise in order to increase the demand.