Through the content you provided above, i am afraid that this book could cover upto the certification level, and as you mentioned that this is for the beginner's level, this could also not be digging into the depth of certification's objectives as they required from very minor to very major information on the topics covered in objectives.
But i am sure that after going through your book one can easily pickup any certification preparation book and can be well prepared for the exam easily which i guess from your discussion above as it provides thorough discussion on all the basic topics covered in the exam.
And would you like to tell us that how much of the exam's objective that book covers, in %age.
Based on the Sun Certified Programmer Exam requirements located here http://suned.sun.com/US/images/certification_progj2se_07_01.pdf
I would say that, with the exception of threads, the book covers all of the fundamental aspects of the exam.
However, and this is true of any Certification exam, merely reading a book that covers the materials is not enough to pass--you need to work with the language, ideally immerse yourself in one or two major projects (and when I say immerse, I mean eat, sleep, and dream in Java), and have a bunch of things go wrong (making mistakes is the best way to become a great programmer--hardly anyone learns well when things go swimmingly fine the first time around).
Hope this helps.