Creation of bubbles worldwide
Trade deficits may sound like something that will only affect the country that incurs it, but really that is not the case. It affects every countries in the world, as we are all trading partners with each other. The dollars that the USA print to pay the exporters for their goods is entered into their country to fuel asset bubbles - and they eventually return to the US as investments, because the exporters don't want to raise the price of their currency by buying in their own currency with the USD. And in turn it creates asset price booms in the USA. It's like an endless loop.
Current account deficits = Financial account surpluses
As I've stated, the exporters don't want to ruin their business. They want to use their existing capacity to the full, and if they dumped the USD on the open market, then it would affect the livelihood of their business.
So what's the point of holding onto worthless pieces of paper? Exporting countries invest the money that the US gave them for their goods back into the US... Confusing, but it is accurately reflected through the current account balance(trade deficit) and capital account surplus(financial account balance), being mirror images of each other.
This fuels asset price inflation both in the exporting country, as it goes through the commercial banking system, as well as the importing country, as it comes back as financial account surpluses.
The world relying on the US running into debt
There must be a demand for goods for there to be money to be made. Over the past few decades American consumption has outweighed its GDP(output), which meant that they were essentially borrowing other countries' output to satisfy their own.
There will be a time when people have enough, and simply can't take anymore, even if you beg them to take out a loan. This has happened with the 2008 subprime lending crisis, as all the prime borrowers are gone, banks are forced to supply loans to subprime lenders.
Deflationary collapse due to excess capacity
In the end, after the bust, there will be a whole ton of excess capacity as there is no demand, and the world will go through a destructive deflationary stage.