In 2016 the U.S. dollar accounts for roughly 90% of all foreign exchange transactions, and 60% of hard currency reserves (according to the BIS). While these figures suggest that the primacy of the dollar around the world is indisputable, the problem with those who want to pound their chest about the position of the dollar is that record global debt loads (in dollars) mean both the U.S. and global economies are in for some rough times.
Specifically, with aggregate global debt higher than it was before the 2007-08 market crash, there's a legitimate concern that trying to pay back debt when (if?) higher U.S. interest rates kick in will lead to a slowing economy.
The only thing I can add is that debt isn't so much the issue as much as what the world is spending it on. With recent events in China (here, here, here, and here), Greece (here and here), and Cyprus (not to mention our trillion dollar war benders in the U.S.) the future doesn't look good.
Put another way, there's a lot of money moving around the world, but we're not investing it in productive activities. Think about it. Market gambles, wealth extracting debt renegotiations, bailouts, and war are not productive wealth creating investments. A small group of financiers may reap the benefits (think Goldman Sachs/Wall Street/Shadow Bankers), but we're still being led down a blind alley of debt.
Worse, just because the majority of this debt is in dollars doesn't mean we're safe. The 2007-08 market crash and the inter-war period should have taught us this much.