The JEDP theory has a lot of mutations, with some people adding other letters, and offering a variety of ideas about when each writer did their work, though all agree that little if any of the first five books of the Bible were written by Moses.

What's wrong with this theory?

It started with certain ideas that further research has shown to be false. In particular, the idea that the books of the Bible could be divided by the use of the two names for God, Yahweh and Elohim, has been found to have reasonable cause that a single author allows. But it was one of the original criteria for divinding parts of the Pentateuch into J and E sections, and now, theorists will either ignore the later research, or else continue to change the theory to keep it alive. One way they do this is by turning "P" into a genie who edited and changed the text at various places for no discernible reason (other than, maybe, to confuse modern JEDP theorists into thinking there was a problem for their theory). For another example, certain features of the text that were once taken as proof for JEDP are now known to simply reflect normal writing practice for ancient people, and thus work with an idea of just one author writing. JEDP also did not conceive of the idea of such things as scribes writing on behalf of others, or of later writers making minor updates to texts to keep them from becoming anachronistic.

Today many scholars still hold to JEDP because they do not know what else to put in its place, and they don't consider Mosaic authorship an option.

For further and more detailed reading:

Specific Case Studies on some texts said to support JEDP:

General Studies

Book Reviews