the major problem with the Mises piece is that Krugman presented his baby-sitting service example is more or less a parable. It's not intended to be an exact parallel, it's intended to illustrate some general concepts. Krugman's education continued long after he had absorbed the lessons of the baby-sitting parable.
The primary concept that the parable illustrates is that small changes in something like the value/supply of money or scrip can affect behavior, even when the people being stimulated or disincentivized are rational, intelligent, well-meaning people.
The objections that the Mises piece brings up are kind of irrelevant. The paragraph that says there's only one way to create wealth completely misses Krugman's point. "Wealth" in this case is created by babysitting. "Production costs" simply don't enter into the picture because it was never intended to be a full and sufficient picture of the whole economy in any event. This is like complaining that the old TV series "Gilligan's Island" doesn't have any sexual relationships between any of the characters. It's not meant to. It's designed to serve a simpler purpose.
Yeah, 'fraid that I, again, am very unimpressed by the level of analysis here.