How valid is the JEDP theory?

Strictly speaking, this is not a theory, but a hypothesis. In scientific terminology, a theory is a well-substantiated, unifying explanation for a set of verified, proven hypotheses. A hypothesis is a suggested explanation for an observable phenomenon, and this is what JEDP is. The Documentary Hypothesis, as originally proposed by Wellhausen, is no longer accepted by the majority of biblical scholars as definitive but, with various proposed modifications under consideration, it remains the best explanation we have for the development of the Pentateuch.

The only serious alternative to the JEDP hypothesis is the tradition that Moses was the author, or at least the main author, of the Pentateuch. For this to be a viable explanation, there ought to be evidence that Moses was a real, historical person and that he was writing from his own experience. This evidence that must be found outside the Pentateuch itself, and could be found by comparing the extensive Egyptian records that we have, against the Book of Exodus. However, Lester L. Grabbe says in Ancient Israel, page 85, there is nothing in Egyptian texts that could be related to the story in the Book of Exodus. Carol A. Redmount says, in 'Bitter lives', published in The Oxford History of the Biblical World, page 63, the biblical Exodus account was never intended to function or to be understood as history in the present-day sense of the word. Perhaps there is an underlying historical core in Exodus but we should expect that a participant in the Exodus would write an account that more closely reflects his experience.

Mark S. Smith says, in his preface to The Early History of God (page xxiii), the older source theory of the Pentateuch (the Documentary Hypothesis) had already come under serious fire when The Early History of God first appeared (First edition: 1990). He says the newer redactional model developed by E. Blume and extended by D. M. Carr on the biblical side, and studies of redaction in Gilgamesh by J. H. Tigay on the ancient Near Eastern side, have complicated source theory without abolishing it. While the death knell for source theory was sounded often over the course of the 1980s and 1990s, it has not been supplanted by a more persuasive model.

Joel S. Baden says, in 'The Re-Emergence of Source Criticism: The Neo-Documentary Hypothesis' that European scholarship abandoned the JEDP hypothesis as American scholars continued to support it. He says this situation is changing, as the Documentary Hypothesis is regaining its place as a viable, productive, and current approach to the Pentateuch. One of the main contributions of more recent source-critical work has been the identification and correction of the methodological problems that plagued earlier scholarship, contributing significantly if not primarily to the move away from the Documentary Hypothesis in Europe in recent generations.

The classic works on the Documentary Hypothesis (DH) are Julius Wellhausen's Die Composition des Hexateuch und der historischen Bücher des Alten Testaments and Prolegomena to the History of [Ancient] Israel (the latter of which, incidentally, is available in English for free via google books). The theory is generally attributed to Karl Graf, but it was Wellhausen who brought it to the forefront of biblical scholarship.

The basic premise of the Prolegomena is the identification of certain contradictions throughout the Pentateuch that point toward a progression toward the "Judaism" of the Exilic and second Temple period. The arguments are very nuanced, but Wellhausen's attention to detail is staggering. Central to his argument is the apprent change of opinion regarding the centrality of Jerusalem for the worship of Yahweh. The earlier strata seem unconcerned by, for instance, Solomon (or Samuel, Elisha, etc.) making sacrifices to God outside of Jerusalem, which is strictly forbidden in the later D and P sources. Moreover, none of the above mentioned people were Levites who were the sole practitioners of the temple cult.

Biblical scholarship has come a long way since Wellhausen, but one would be remiss to toss out his work as passe or otherwise "disproven." The DH is broadly accepted by nearly every serious scholar of the Hebrew Bible (with modification and individual nuance, of course) for good reason.

Don't accept (or reject) the theory just because someone on the internet said so; read the first few chapters of the Prolegomena (with a Hebrew Bible next to you if you can)--the man was truly brilliant.

Post Script: Incidentally, Wellhausen was a devout Christian--keep that in mind when you read about his theories.