Waldo lives on a space station orbiting Earth, because he was born with a rare condition, myasthenia gravis, which has made his muscles extremely weak, and he is much better able to cope with life in zero gravity. He's quite brilliant, and highly arrogant, so consulting him tends to be a last resort.
In the course of figuring out what has caused the deKalb failures, Waldo is forced to travel to earth to consult an old man who has managed to make one of them work again...by magic, apparently. He teaches Waldo about the Other World, which he describes in somewhat mystical terms, but Waldo returns home and comes up with a theory about parallel universes that explains the phenomenon adequately for the purposes of repairing the device, though the solution can only be employed by someone with the right mental attitude (back to some of Heinlein's ESP musings again).
One rather interesting passage:
"Suppose Chaos were king and the order we though we detected in the world about us a mere phantasm of the imagination; where would that lead us? In that case, Waldo decided, it was entirely possible that a ten-pound weight did fall ten times as fast as a one-pound weight until the day the audacious Galileo decided in his mind that it was not so. Perhaps the whole meticulous science of ballistics derived from the convictions of a few firm-minded individuals who had sold the notion to the world. Perhaps the very stars were held firm in their courses by the unvarying faith of the astronomers. Orderly Cosmos, created out of Chaos - by Mind!"
Still not sure whether it's an apocryphal story or not that Heinlein was the one, in this book, who coined the term "waldo" for remotely operated manipulating tools, still used today.
The second story is, on the surface, about a businessman's struggle against a protection racket run by magical mobsters, and then against a professional association for magicians which threatens to wipe out all competition in the area. Actually, it seems to be a product of Heinlein's foray into politics, and either reflects things he saw happening around him at the time, or events he thought might come to pass - just without the magical twist that made it a story publishable by the pulps he wrote for.
Some good fodder for thought in this one.
I found it interesting what he had to say about gun control, over sixty years ago.
"I see the drawbacks of magic as well as you do," he went on, "but it is like firearms. Certainly guns made it possible for almost anyone to commit murder and get away with it. But once they were invented the damage was done. All you can do is try to cope with it. Things like the Sullivan Act - they didn't keep the crooks from carrying guns and using them; they simply took guns out of the hands of honest people."
Sound like a familiar bumper sticker, anyone?