For instance, I think that gold has really very few intrinsic value,
Gold and silver both have excellent industrial characteristics. They are both excellent conductors, for example, with silver being the best elemental conductor known to science; and gold does not corrode even in harsh environments such as under the ocean floor. Both are used extensively in electronics for space, and gold is used as a coating for glass windows, because it can filter out radiation and solar intensity much better than leaded glass. Silver is also traditionally used in dishes because it has antibiotic effects, not because of it's color. Polished lead can look almost as shiny, and that would not turn out as well. Pure silver is not the only material that inhibits surface growth, but the only one known of before 1965, and still one of the better methods, and used in medicine to this day. Silver is an excellent heat conductor as well, and used in heat paste to dissipate the heat of a computer's cpu. Silver can be used to make better batteries, but they would literally cost a fortune. Gold would make an ideal material for bullets, because it's more massive than lead, non-toxic to any form of life, and as soft as lead and therefore as likely to 'mushroom' effectively.
The point here is, the main reason that we don't see these uses is because of the monetary value of gold, not because it isn't useful. The 'intrinsic' value doesn't have to add to, nor equal, it's monetary trade value; only provide for a natural price floor.
Actually I think that the fourth characteristic should be replaced by the "hard-to produce" aspect, or scarcity.
Scarcity is not a characteristic of money, because it's trade value adjusts to it's scarcity. Historicly; gold, silver and copper coins were all inter-traded, but copper wasn't particularly scarce. Iron/steel was more valuable during the middle ages, because kings had a hard time outfitting armies with weapons made of copper. Steel cooking pots would have been considered expensive. One contributing cause was that refinement of quality iron required much more energy and labor than copper, silver or gold. All of those being softer metals, and therefore much less labor intensive than iron or steel. These days, refined gold "above ground" is less scarce than silver of a comparable condition; yet gold is many times more valuable because of it's monetary value, which silver lost along the way.
Taken on the other side, platinum is much scarcer than gold, and today is much more valuable because there are industrial uses for which there are no acceptable alternatives, not because of any monetary value. The miners were aware of platinum by the 1600's, but Spanish treasure ships were likely to forge it into a ship's ballast weight, a cannon, or even a cannonball rather than use it as money. It was scarce stuff, and they knew it, but they didn't have any special use for it, and is was
too scarce to attempt to make it into coins, because it was so scarce that most people had no experience with it, and would therefore be unlikely to be willing to trade in it at all. Mercury was often found in silver (which is why it was called quicksilver) but also often found with platinum. Mercury was significantly more valuable than platinum because doctors of the day believed it had medicinal properties.