A great deal of effort has gone into dating and sorting out the various parts of the Zhuangzi. This can be an important exercise in as much as it helps us to better understand the book as a whole and how one part might inform our understanding of the others. We must also remember, however, that what we do understand of the philosophy contained therein is that there comes a point at which we must psychologically toss aside the fish-trap after catching the fish. Or, as Zhuangzi longingly pleads, "Who has forgotten words that I might have some words with him?" He would, in fact, have enjoyed the discussion about this book that bears his name, but he would not have missed its message which goes well beyond words.
This having been said, I will now sum up the conclusions reached by Liu Xiaogan in his important study Classifying the Zhuangzi Chapters. For the most part I think we can say that his conclusions tend toward the traditional understanding of dates and authorship with the notable exception of his recognizing that there were in fact many authors. (Amazingly, it was not until rather late that commentators such as Wang Fuzhi (1619-1692) began to question the authorship of Zhuangzi for the entire book.) I won't relate his evidence for these conclusions except to say that they mostly deal with word usage, historical references (in and to the Zhuangzi), and style. None of his conclusions are definitive, but only strongly indicative of a tentative position.
The Inner Chapters (1-7) were written in the Mid-Warring States Period, which is to say during the time of Zhuangzi (ca. 369-286 B.C.E.) who can thus be assumed to be their author. These chapters evince a significant inner coherence that suggests their having been written by one hand. This also dismisses the idea, promoted by A. C. Graham, that they were "cobbled together" by an unknown editor or editors. (Liu also takes strong exception to Graham's assertion that they are "mutilated" and especially to his presumption to have added passages from other chapters to 'reconstruct' them.)
The Outer and Miscellaneous Chapters were all written at the end of the Warring States Period and before the Qin Dynasty (221-206 B.C.E.). (Many scholars believe that some chapters were written in the early Han (206 B.C.E.-220 A.D.))
The actual compilation of the book (delivered to Guo Xiang (252-312) as 52 chapters and pared down to our present 33) took place shortly thereafter. The various titles were also assigned early on, many, especially those of the Inner Chapters, possibly at the time of the chapters having been written.
The authors of the Outer and Miscellaneous Chapters were many, but were all what today we would call of Daoist persuasion. (This too differs from Graham who suggests 4 schools: Zhuangzi (“Daoist”), Primitivist, Yangist, and Syncretist.) Liu has 3 groups: Transmitters of Zhuangzi, Huang-Lao (a more social adaptation), and Anarchist.
You can check out Scott's writings on Zhuangzi here.