The law gives the Secretary complete discretion over everything having to do with the minting of platinum coins. This is very likely an unconstitutional delegation of the legislative power to coin money and regulate the value thereof.
Of course, the Court could sidestep this issue by simply declaring that the law doesn’t really do what it seems. As Kevin Drum argues, the law could be interpreted as creating only the power to create commemorative coins issued for collectors and platinum investors. I don’t think this is a very good way of reading a straight-forward statute but it wouldn’t be the first time that federal courts interpreted laws in creative ways to avoid finding them unconstitutional.
One question about this, however, is who might have standing to sue the government over the issuance of a $1 trillion platinum coin. The federal courts hold that a plaintiff must be able to show that he has suffered or will imminently suffer injury in order to have standing to sue. For these purposes, it’s not good enough to be, say, a serious advocate of the non-delegation doctrine. Your injury cannot be purely ideological.
I suppose that workers at the U.S. Mint may have standing to sue in order to avoid being forced to commit an unconstitutional act.