I'll start with the good; the Paleo diet overcomes a lot of the weaknesses of other diets in that it does not demonize the eating of meat; as such, it has a degree of balance that many other diets do not have.
On the flip side, is it really "Paleo"? Biblically, I think not; the Scriptures describe men as more or less fruit-eaters prior to the Fall, and than afterwards eating what grew in the fields--I would presume that this means grains and legumes primarily. Hence, pointing back to "cave-men" does not really point to what is the oldest, as the true "Paleo" diet would be Adam's and Noah's vegetarian diet.
That said, I could envision people after the flood going to a "Paleo" diet--the modern version, not Noah's--by killing and eating most of the nastier animals whose physical traits would help humans to "assume environmental temperature," if you catch my drift. Moreover, as people filled the earth and subdued it, they necessarily moved to places where grains and legumes would not grow, and thus necessarily became rather carnivorous. They were still descended, however, from vegetarians.
Going to the New Testament, my take is that I have trouble with the idea that our Lord would include panem nostrum cotidianum da nobis hodie (Give us this day our daily bread) in His prayer if that were indeed a substance harmful to most people. Yes, there are people with gluten sensitivity and wheat allergy and such, but the fact of the matter is that almost all people get large portions of their nutrition from grains, and it hasn't exactly made us extinct yet.
So whatever its virtues and deficiencies, I'd simply encourage believers to recognize that Biblically, the "Paleo" diet is not really the paleo-diet, and when "Paleo" advocates decry grains, they're on dangerous ground, Biblically speaking. And since my hungry monsters (and their father) have devoured today's batch of pain ancienne, I'm thinking I'd better get up to the kitchen to knead some more, 'cause we