In introductory economics students learn that in a system of floating exchange rates (like the one we have), trade deficits and surpluses are eliminated through changes in the exchange rate. That is the point of the float. This means that if a country has a trade deficit, like the United States, then we should expect its currency to fall.
This means that when countries that complain about the U.S. trade deficit complain about the decline in the value of the dollar, as the NYT claims is the case with Germany, China, and Brazil, these countries are saying that they don't understand economics. In this case, the news is that major economic powers are being governed by people who don't know economics.
This would be like countries promoting their exports and then complaining that foreigners were buying up their output. If these countries want the United States to reduce its trade deficit then they want the dollar to fall. There is no other plausible mechanism to reduce a trade deficit. In the article the drop in the dollar is described as the "easy way out." It should also have been described as the "only way out."
The article also notes complaints from other countries that the low interest rates resulting from the Fed policies may lead to bubbles in their economies. Insofar as this is true, these countries are in fact complaining about their own poor economic management. Low interest rates, like low food and energy prices, should promote growth, not impede it. If countries consider low interest rates harmful to growth, it suggests that they have a poorly structured economy.
This article also refers to the United States' "addiction to debt." This sort of bizarre criticism (it is not supported by anything) belongs on the opinion pages, not in a news article.