What both books get horribly wrong is what all such do: they vastly overestimate how quickly space travel would occur and they totally fail to predict automation, computers and the like. For example, von B has a Hubble-like space telescope floating in space: but to use it, you have to visit it. And you point it by hand1. For example: von B has an expedition to Mars... but not preceded by any robot probes. von B also has canals on Mars, but never mind, they are going to be part of the story, I can forgive him those.
Clark has his boyz head off from Earth for Mars, in a ship rather reminiscent of an English steamer, but I think stuffs up the orbital mechanics. After leaving the jolly old Earth behind, he is saddened when Earth eventually becomes invisible, blotted out by the solar corona. Because of course the path from Earth to Mars is outwards, and so Earth and the Sun will be in line. Oops. von B, by contrast, as you'd expect gets the orbital mechanics right - at least as far as I can tell - but goes wrong in my highlight, where he is explaining temperature maintenance in space (aside: very quaintly, his space station is powered by solar power... but by steam solar power: a mirror boils water, and the spokes of his space station wheel serve to condense it).
This is radiative physics, and somewhat reminiscent of The idealised greenhouse effect model and its enemies. The easy one first: a fully reflective sphere at all wavelengths with no conduction will neither absorb nor emit radiation, and so will maintain whatever temperature it starts with, whatever that might be; there is no "temperature of equilibrium" because there is no transfer to permit equilibriation. But a fully black sphere at all wavelengths (idealised to have a superconducting surface, unless you want to think about the temperature distribution) will not. It will have some equilibrium temperature; if you start it hotter it will cool down, if you start it colder it will warm up. This, incidentally, is from page 93. On page 94 we find the statement that a mirror-polished spaceship will simply retain it's temperature, which is much better, though slightly wrong, because of course the people inside and equipement will emit heat, so it will slowly warm up. So p 93 might be an oversight, or perhaps a translators error; but probably not, because the same error occurs just a little above my quote.
Update: it turns out that Martians exist. They live entirely underground, but their pumping of water from the poles is visible. They are entirely benevolent and more advanced than us, but in need of rejuvenation. There are some tedious dialogues about religion and stuff that I skipped. Despite being more advanced, the Earthmen learn nothing from them; in turn the Martians have at no point listened to Earth radio broadcasts. The return-to-Earth happens with no assistance from the advanced Martians, presumably because von B wanted to prove his point that it could be done.
1. Its also not in constant use. It seems to be available and unused whenever our heroes happen to want to look at it.
2. Also, his propellants are hydrazine and nitric acid. Failing to think of liquid oxygen is odd, I think. For propulsion, that is. There's liquid oxygen for cabin air.
3. Page 102: it turns out that the guidance for the ships will be calculated by giant electronic super-brains, and stored on thousands of magnetic tapes, which tapes will be carried aloft and run by hand through the ship's course-correction facilities. Though a super-special lightweight machine was also to be carried, capable of producing tapes en route.
4. There's also some stuff about nuking the Commies into submission, so cue Tom Lehrer.