How to evaluate a book, rather than a paper, on a scientific subject? In academia we collectively evaluate the validity, quality and significance of shorter publications - papers - with a complex system of conferences and journals. With all its flaws, you can get a typically-not-so-bad idea about those aspects of a published paper by looking at things like venue and citations.

But that's not the case with books. I don't have any experience publishing books, but obviously it's not the same process as for papers.

Now, suppose I've entered a field which I've studied through papers; and I now want to either teach from a book, offer it to someone for some concentrated self-study, or cite from it. Also suppose I have some specific books I'm considering. How would I obtain some sort of evaluation or review of them, overall or by specific criteria such as correctness of proofs, rigor, clarity, narrative flow, being up-to-date etc.?

Note: Of course you can evaluate a book pretty well by reading it, but the idea is to choose what to get and read.
Obviously, this question asks about reliable predictors for the quality of a book. Otherwise the answer can only be: You evaluate a book by reading it. With this out of the way:


Ask around. In particular when you are interested in using a textbook for a course, ask people who have directed similar courses.
Publishers. There is an informal hierarchy of publishers that can be used to predict a book's quality, just like conference venues and journal ranks for papers. This differs between disciplines, but the edge-cases are vanity presses (low-end) and Famous University Presses™ (high-end).
Citations. Just like for journal articles you can count the citations of a book to estimate its impact (with all the known caveats).
Reviews in journals. Many journals publish a review section. You can search these for discussions of the book that you are interested in.
Peer review. Some publishers also send full book manuscripts or at least the book proposal with sample chapters out for peer-review. 
Professionals. Ask your trusted librarian for advice.