Yes, the United States dollar should remain the world's default currency as it has been for quite some time now. Replacing the dollar could be disastrous on the world economy, so even if the dollar is a bit weak, there is little reason to risk global economic crisis by switching to a new currency.
The US dollar should not remain the world's default currency. The US government has been spending almost a hundreds of billions of dollars per year more than it brings in for the past decade. Raising taxes to pay for government expenditures is not a popular move. The easier method is to simply print more money. As the amount of money in circulation inflates, its value goes down. It is simply supply and demand. Inflation is like a silent, stealthy tax on not just Americans, but everyone that chooses to use US dollars.