The problem with precious stones is that the vast majority of people don't know what they are actually worth and most of us don't even know what stones are really gemstones without some sort of reference book. Diamonds are vastly overvalued and are intrinsically worthless to the average person, I believe the same would apply to any gemstones in the post-apocalypse world.
As for precious metals, platinum and palladium are so rare in the marketplace that it is highly unlikely most people will ever deal with them except as jewellery. Even then, most people have no clear idea of how much they are worth so I doubt many people would accept these metals in trade if for no other reason than the fact that most people would not even recognize them for what they are when they saw them. In fact, platinum is not even sold to the average person off the street and in nearly every 1st World nation, someone trying to buy/sell it without a legitimate dealer's licence is going to be investigated by the police (I have a friend who works in the mining industry, platinum is such a controlled metal that the company he works for requires a licence to possess a minor amount of platinum)
Gold and silver are very different, easier to mine and refine and almost universally recognized as gold or silver. Both can be valued reasonably accurately by simply weighing them as they should both be about 99% purity when cast into ingots. The other metals are much harder to judge because who really knows the weight expected from an ingot of pure palladium except for an expert or metallurgist?
But I do believe their value will be based entirely on whether someone is prepared to accept them as trade because they will be hoping (indeed, "banking" on the idea) that the money market will re-establish itself and the gold/silver will be worth something in the future.
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