These criticisms of the Documentary Hypothesis are taken from Gleason Archer, A Survey of Old Testament Introduction, 113-116, with comments in italics added by me.
For an brief summary and explanation of the documentary hypothesis from a Christian perspective, click here (don’t forget to come back here when you’re done!).
1. It uses circular reasoning by positing its conclusion (the Bible is not supernatural revelation) as its underlying premise (there can be no such thing as supernatural revelation). Another example is their picking out portions with similar styles, proclaiming that these portions all belong to one document, and then appealing to this new “document’s” remarkable consistency.
2. It is allegedly based on the evidence of the text itself, but when the evidence of the text goes counter to the theory it is consistently evaded. They often evade it either by blaming a later redactor (R) or by claiming the evidence is a later invention.
3. It holds a subjective bias in the treatment of the Hebrew Scriptures as an archeological document. It is an ancient document, which means it should be viewed as an archeological document, but instead, it is not regarded as an archeological document, its information is discounted because it is a “religious” document.
4. It fails to consider the exceptional character of Israelite religion as monotheistic from start to finish. There is no record of any religion that changed to monotheism.
5. It practices eisegetical interpretation of texts to produce “discrepancies” that “prove” diversity of sources. An example is the death of Sisera; in one chapter (Judges 4) he is said to have been killed while sleeping, but in the next chapter the song about his death mentions that he asked for water and was brought milk. However, the second text does not say that he was drinking milk when he was killed. This is a fabricated discrepancy.
6. It assumes that modern European critics can confidently determine the date of composition of each document, despite no other comparable Hebrew literature for comparison. We have no other contemporary Hebrew literature to compare it to.
7. It assumes that modern scholars can more reliably reconstruct the way things really happened than could the ancient authors themselves. This arrogance is the result of the modern scientific worldview.