Is there some book or other reference that I can cite as a catalog of NP-complete problems, more up-to-date than the appendix of Garey&Johnson's book? I don't want to cite web sites, even though I know there are some excellent compendiums om the web.
There is "Encyclopedia of Algorithms" from 2008, which surveys a lot of different problems (1160 pages of it)
I know you want book, but I think in this case Wiki is good, You can download it with depth 2 to have list of problems and their definition, Also I think Gary and Johnson book is good enough to be familiar with problems, after that you just should find your interest and work on it, there is no need to know all problems and their solution. Also reading first papers of your interest problem is good, you can find what was the first idea, after that may be solutions become better, and in books you will find best solution not philosophy of solution.
Also there are some new problems like matroid secretary See this, and I think this new problems (and newer) just available on web and papers not books.