Okay, I'm done.
Now, let me just say that I didn't like The Long Earth all that much and I hated The Long War, so I went into this with equal parts low expectations and dread.
I will say I was pleasantly surprised. I think Baxter (and I do think that Baxter is doing 90% of the work here; I see very little Pterry here, other than ideas he might adding) listened to the hundreds of negative reviews and got rid of the endless chapters of backstory and exposition that made TLW so incredibly dreary. The Long Mars is much more plot-driven, which is a good thing.
The two separate journeys--one with Cap'n Kauffman going where no Long Earth has Gone Before and Sally and Dad's journey along the long Marses (Mar's? Mars'? Marseseseseses?) are the best parts, since the focus is on exploration rather than the dreary social/politic posturing that drags down so much of the series in general.
But there are many parts of this that stretch credulity or simply steal ideas from other books. The "elevator to the Heavens" has already been mentioned. And it really makes no sense that Lindsay Sr. would absolutely predict it would be there. To make that assumption, he had to be certain that technologically advanced life would definitely have evolved on Mars--a long shot at best.
But I find the "science" behind the evolution of life on the Long Marses to be totally hogwash. It took 200 million years for technologically advanced life forms to evolve on Earth, and 5 million or so for humans to evolve from monkey-like mammals. Yet, on these Long Marses, where life exists only during short periods (say less than a million years) when volcano eruptions replenish the atmosphere and melt water, creating an environment for space parasites to fly from dead creatures who "fell" into the Gap from adjacent worlds, advanced life emerges after thousands of years. Perhaps it's possible, and perhaps different natural selection processes drive evolution on Mars, but remember that we human beings are only here because a meteor knocked out the dinosaurs. So the odds of many different sentient species evolving on alternating hospital/dead Long Marses seems very, very far-fetched. Unless, of course, a higher intelligence is guiding evolution on the Long Marses. I also find the idea of stepping and traveling via gliders to be totally bogus. One would think that sandstorms would have been in full force on half of these Marses, making the odds of a glider surviving almost negligible.
As for the Kauffman journey, it seems to be one huge MacGuffin for the discovery of the Next living on the wreckageof the crashed longship. They go as far as 300,000,000 Long Earths and turn around. Oh, and then they put the eccentric billionaire (who seems to be based on the eccentric space-funding billionaire from the book/movie Contact on his own planet for the very rich. Grey Poupon, anyone?
And the whole Next thing is pretty tired SF. Theodore Sturgeon did it decades ago in More than Human. Star Trek did it to death in the Khan & Company stories. It's just dull superman type stuff and doesn't add much other something for Joshua to do since his marriage is kaput. And it creates yet one more bogeyman for the witch-hunting Datum Earthers to hate. For it's the steppers. Then it was the Happy Landings hippies. Now it's the supermen. It's always something.
I'm also getting a little tired of the incongruities of this series. For example, in the first two books we learn that many Earthers can's step. Neither can the beagles, apparently. But if Snowy could "step" by traveling on the airship, then why didn't someone ship out all those non-stepping Datumers (like the little psycho kid left behind by his family) on the airships as well to be reunited? Certainly Lobsang would have known this was possible.
And how was Lindsay Sr. able to communicate with the Long Marsers? For god sake, we humans can barely communicate with people who don't have a 100% understanding of our own language. Yet with no problem at all he's able to approach a bunch of totally alien beings and communicate his "deal", the idea of stepping and how to use the boxes and exchange this for photos of the monoliths in a matter of an hour or so? Hornswoggle. Unless we find (and I'm pretty sure that will come out) that Lindsay Sr. is a Next. He certainly possesses most of the characteristics of the species.
Oh, I don't find the reuse of the crab kingdom from the Science if Discworld book to be particularly clever. In a book that borrows so many idea from other sources, couldn't they have found another way to convey a different kind of intelligence? How about smart ants? Snakes? Pigeons?
The book is enjoyable if you're willing to suspend every possible kind of disbelief. But Baxter tries to hard to make the science plausible in some areas, while letting the truly implausible go without comment.