The hypothesis (H): the text of the Torah is composed of fragments written by different authors at different times which were assembled into a single document by a later editor.
The evidence: (a) variations in literary style - most prominently different names for G-d, plus different forms of verbs, numbers, etc.; (b) contradictions; (c) repetitions; (d) reflections of different conditions of composition.
Evidence for a hypothesis is evaluated in terms of its competitors. The competitors for (H) may be (I) The text of the Torah was written by a single person or (J) The text of the Torah was dictated by G-d. The evidence cited relies upon human psychology: a single human author would not use features like (a)-(d). Thus the evidence counts for (H) against (I). But it is irrelevant to (J): we have no basis of comparison for "Divine psychology." Compare the suggestion that it was written by a single Martian. (Of course, (J) will have to explain that part of (a)-(d) which is genuine - see the standard commentators.)
The evidence for (H) against (I) relies upon our very sketchy) knowledge of the psychology of authors of 2500 years ago.
The identity of the editor and the event of the amalgamation of the separate sources into one book is inexplicably missing from the historical record.
Documents from the same period vary names of the same god.
(H) accounts for (b) and (c) by assuming an editor whose piety prevents tampering with the fragments. But (a) reveals cases where the editor must have interwoven texts and changed the style so as to avoid to obvious uniformity within sections. This contradicts the editor's piety. Solution: two editors! The first is too pious to change, the second changes! With this kind of flexibility (H) becomes irrefutable (that's bad).
The Technion project: computer literary analysis of Genesis gives highest probability of one (even human!) author. They note that only variations in style of which the author is unaware can count. (If the author was aware of the variations, he may well have had a reason for them which we, so removed in time and culture, would not understand.) But then, how could we possibly know that the author was unaware of the variations?!
The Bar-Ilan project: the stylistic "signature" of an author shows in the frequency of adjacent letters. Genesis is consistent enough with respect to this type of signature to be regarded as having a single author.
Archeology refutes (H)'s explanation that patriarchal Genesis is anachronistic projection of later living conditions: the general living conditions in the patriarchal period agree with Genesis, and not with the living conditions in the later periods in which the stories were supposedly written.
Further reading: Cassuto, The Documentary Hypothesis (Jerusalem, 1961); Bronner, Biblical Personalities and Archeology (Jerusalem, 1974), Genesis – An Authorship Study, Yehuda Radday and Haim Shore, Analecta Biblica no. 903, Loyola Press, 1985.