First, it's old. It was done in 1963 and won't be revised, since the author is dead. It thus has a very "traditionalistic" selection of texts, with philosophy more narrowly defined than I feel comfortable with. And of course, it doesn't include any of the textual discoveries since 1963, or any of the groundbreaking textual work, such as Graham's on the Chuang-tzu. There are major authenticity problems with some of the selections from the Kung-sun Lung-tzu and Tung Chung-shu as well.
Second, even for its time, it's conservative. The author was, to put it kindly, credulous about some early datings. The discussion of the Lao-tzu is particularly problematic. There is also an overly dismissive attitude towards the thought of some periods, such as the Han.
Third, it's somewhat biased, though in a very traditional way. The Neo-Confucian standpoint is more or less assumed true throughout. This detracts from the discussion of some documents earlier than the Neo-Confucians.
None of this is an argument not to use the book. But be just a bit careful if you do.
That being said, this book also has serious limitations. Arbuckle's review (which is nearby) expertly identifies many of them. Here are some more. Chan's English is much better than my modern Chinese, but he still sometimes lapses into incoherence. With a few exceptions, his comments on the translations are both confusing and confused. Chan likes to use Western philosophical terminology, but he is not in command of it. It is neither accurate nor helpful to describe the Ch'eng-Chu wing of Neo-Confucianism as "rationalistic," and the Lu-Wang wing as "dynamic idealism."
For many of the philosophers that Chan covers, this is still the best source for translations. This is especially so of later Chinese philosophy. I know of no better translation of selections from Ch'eng Yi and Ch'eng Hao, for example. But for many other philosophers, you would be better off with translations with a more narrow focus. Daniel Gardner's _Learning to Be a Sage_ is a great source on Chu Hsi. And I would (not surprisingly) recommend the anthology I co-edited for translations from ancient Chinese philosophers. (D.C. Lau, Victor Mair, and Burton Watson have also produced more extensive translations of major early Chinese philosophers. Look up their names here on amazon.com.)