How valid is the JEDP theory? The JEDP theory basically states that the first five books of the bible (the Pentatauch) were not written by a single person, but rather by four different people.  

I'm trying to understand if this theory is even remotely valid or if it is complete nonsense.

Specifically (to avoid this being closed as argumentative), what are the most reasonable supporting arguments for this theory?  Also, what are the major criticisms against this theory?
The JEPD theory was developed in three stages, which I summarized in my answer to 
What was the reasons for documentary hypothesis?. It isn't complete nonsense; it's the culmination of several centuries of Bible scholarship. Whether it is a giant leap forward or a brilliant mistake, I'm not certain.

On the one hand, it's rational, and it fits different types of writing into neat categories. It has a ready answer for things that might be hard to explain otherwise. 

On the other hand, it's highly speculative. I've found that it is trivially easy to look at any source text and find inconsistency. I myself have tried this method and "discovered" evidence of multiple sources in Richard Dawkins' The God Delusion. 

Perhaps the most serious scholarly argument against the JEPD hypothesis is that it doesn't explain why a later editor would bring all these sources together, if the traditions had kept them separate. The more likely scenario, according to this argument, is that the doublets and stylistic differences were part of a tradition that began with Moses and accumulated over the years.