I don't know that I've read much Spider Robinson before; maybe a few of his Callahan stories. I have read a lot of Robert Heinlein - most of what there is to read. So I can say with a high degree of confidence that Robinson did a masterful job of producing a new Heinlein novel based on an incomplete outline and some notecards Heinlein produced way back when, and never wrote up. This book sounds like Heinlein, in small ways and large.
Unfortunately, Robinson also reproduced the mid-period Heinlein's machismo and some of his less appealing quirks. Our hero is all for equality, and for sexual permutations of all descriptions, but obviously the best way is for real men to lead, right? Women are brilliant and strong, but when it comes to the tough choices, that's when the man steps in to save the day and the damsel. It's a flaw that worsened in Heinlein as he aged, until it became almost a parody of wish fulfillment. Here, Robinson gives us not a Sail Beyond the Sunset Heinlein, but a Glory Road version. It's a perspective that hasn't really aged well.
The fact is that Heinlein was really best at short fiction. Some of his novels are excellent, but the bulk are just adequate and now dated, where much of his early short work still stands strong. Robinson has done a good job with the task given to him, but I frankly would have preferred a book that assumed Heinlein had finally modernized his attitudes than one that replicates 1950s views in the 2000s.
The book is generally a quick, enjoyable read, despite the ponderous, often chauvinist philosophy. Robinson does make some missteps, such as with extended plugs for current artists and a few others. And he does very little with the characterization - key figures are very Heinleinian, but they're not very deep. The ending in particular is shallow, as are the motivations of some of the characters in it. Robinson sees this a one of Heinlein's juvenile novels, but young adults are sharper and deeper than he (or Heinlein) give them credit for.
All in all, the book is unsurprising. It was a better clone of Heinlein than I expected, but not a better book. If you miss Heinlein's voice and politics, here's a chance to see them one last time. If you want a light, male-dominated adventure story, feel free to pick this up. But as SFF has matured over the years, the quality of the content has matured with it, and I'm sorry to say that run-of-the-mill Heinlein just isn't at the top of the heap anymore.