Deflation would be the biggest problem, deflation is the depreciation of money. Another way to look at it is that if you have a surplus of something it will have less value.
There would be several problems if all states decided to print their own currency. For example, international trade would be very difficult, if not impossible. It is likely that each state would have to trade independently. This would be particularly difficult as the federal government oversees international trade. Moreover, trade between the states would also become difficult.
Such a system would also put us in a difficult financial situation. Money would not longer be unified, which might prove problematic for the federal government in issues such as budgeting and taxation.
