The reviewers that give low-star reviews seem to be missing the subtitle of the book: "an introductory survey." The first two sentences of the preface explain Heath's standpoint for the entire book- a broad overview of numerical methods, with focus on the ideas behind the algorithms rather than detailed analysis. There are certainly other materials out there that go into much more depth than what Heath does, but that isn't what he was trying to do. Topics in the book include basic numerical analysis, linear equation solvers, least squares, eigenvalues, nonlinear equation solvers, optimization, interpolation, numerical integration/differentiation, IVP/BVP ordinary differential equations, partial differential equations, and briefly, FFT and random numbers.
I consider myself well-versed in numerical methods, even before reading this book. I still learned many things from the book though, which is either a "plus" for Heath or a "minus" for every other numerical analysis book I've looked through. Heath always discusses existence, uniqueness, and conditioning of problems in very well explained math- as an engineer, I found the proofs and derivations easy enough to follow. The discussion of implementation is always in pseudocode, and only hits the main points of the algorithms- this could be better by mentioning some (or more, if applicable) of the problems that come up, such as scaling and error issues.
My complaints with the book are 1) the overall organization, including the fact that all throughout the book Heath says "as seen in section x.x" (clearly, the man is a Fortran programmer- these are just GOTO statements); seriously, I know how a table of contents and an index work, 2) a lack of non-trivial examples; I think one or two big "case studies" or something similar per chapter would really help to cement the material and its implementation. Also, 3) the book is on the expensive side. I learned a lot, but if I were to normalize by cost, I didn't get much value from this purchase.
So in summary, the book is good but not outstanding (I don't think there is an outstanding broad-brush numerical analysis book yet). The math and theory is just right for people seeing this material for the first/second time. The examples are kind of lacking. If you write scientific software, this is definitely one to get.