The short version: Good system, badly edited, blah setting (mainly due to presentation). Mainly worth picking up if you're looking for the tools to run your own BRP or Openquest space setting.
River of Heaven is a frustrating book. The Basic Roleplaying lineage has a real shortage of solid science fiction implementations, especially if you're only counting ones in print or that aren't just Call of Cthulhu with spacesuit rules. So River of Heaven is really welcome for that reason. It uses the Openquest variant of BRP (one of my favourite versions of Basic Roleplaying), adapting a lot of the rules for firearms combat from the earlier Openquest setting-supplement The Company and adding spaceships / vehicles, bodily augmentation and a variety of biological types (genetically augmented humans, space-born humans, androids, etc.). Like all Openquest books, it's standalone, so you don't need a copy of the Openquest core rules to run River of Heaven games.
Though it has a particular setting associated with it (mostly detailed in the back of the book), you could easily adapt the system to your own science fiction campaign setting. In fact, my recommendation is to do so. If you wanted to pull out your old Mutant Chronicles books, this would be a good system to run games in that setting with.
The default setting is not terrible, but you get a lot of weirdly unplayable information about it, at the expense of interesting things to do. In general, the presentation veers towards physical details about the planets and stars, at the expense of the social geography, which is described only briefly for each one in longform text. I would rather know the capitals of the planet's polities than the metallicity of the star it orbits around, especially since the latter information is available on Wikipedia. The beginning of the major interstellar conflict that will eventually plunge humankind into a new dark age is briefly outlined in a planetary description that doesn't mark it out as particularly important or interesting (you will only realise it's the beginning of this conflict if you read two other parts of the book). This is not the only example of something being buried in a way that makes it hard to piece together.
The overall presentation of information leaves you grasping to pull it all together and make sense of the bigger picture or to get a clear idea of what your PCs could do that's particularly interesting.
The setting also has something that is purely a personal issue, and which may not bother you: A religion whose only religious doctrine appears to be "AI is bad" (the "Renouncers"). It's clearly a nod to Dune, one of the main influences on this game, along with Alastair Reynold's Revelation Space series. But it's a terrible science fictional trope, because it's unclear why anyone belongs to the religion. Why do they think AI is bad? Why are they a religion and not a political group? The Renouncers are set up to be major players in the setting, but we get only a few scraps of information. The cool alien villains that nearly wiped out humanity and that everyone is terrified by and the AI uplifters are also underdescribed, though at least one gets stats for two kinds of machine avatars.
The overall effect of the choices made about how to present this setting left me feeling unenthused about it. I don't think it's bad or stupid, it's just got an extremely weird focus about what information it wants to tell you about itself, and that focus doesn't sell it very well.
Production-wise, the book is both very pretty, and very, very badly edited, though there is at least one incomprehensible design choice. It's printed in full colour bleed, and the colour choices are well-made to improve readability (black text on a grey background). D101 books are almost always badly edited, but this is the worst one yet. Text is repeated both in headers, and most obviously, in the double-listing of PDAs in the equipment section. Some sentences, luckily mostly descriptive text rather than rules, are simply gibberish that look like half-finished rewrites. Tables have inconsistent spacing from the text around them. And in the combat section, several rules are just wrong or missing - the rules for double-tapping refer to hit locations (a thing the Openquest variant of BRP does not have) and there is no actual rule for determining how many shots in a burst hit the target despite the text telling you to roll to determine this. As well, it has the usual Openquest ambiguity about whether characters can dodge ranged attacks, with the dodging rules saying "No" unless they're hand-thrown, while various other spot rules mention doing so.
The incomprehensible design choice is to have five different sidebars on five different pages of the equipment section contain various sections of rambling in-character essay about tea (with a "Cont on pg. XX" at the end of each one). It looks like it was filler for various pages that had large tables on them and that couldn't fit a second table, but I'd rather just have had blank space, or at least a listing for tea in the "Food and Accommodation" table.
Like I said, it's a frustrating book. I do think there's a solid core here, especially with regard to the system, though the lack of editing gets in the way of it at times. It's worth picking up if you're looking for a BRP science fiction game and are willing to basically tear the system out and use it as a toolkit to run your own space adventures.