I've been watching for several years now (I adopted the diet myself in 2010), and all of the negative critiques tend to fall into (a) critiques from non-experts, (b) critiques from experts in unrelated fields, (c) health experts who agree that his recommendations have merit, but that they're impractical for the general public to follow.

I produce for you a book written by a relevant expert with ~2.5 times as many references as The China Study (2034 vs 758) who advocates eating an ancestral diet (lean unprocessed meat/fish, fruit, nuts, vegetables/root vegatables) (1). A list of individuals with relevant graduate degrees who more-or-less agree with him can be found in this list of speakers at a paleo conference he spoke at. His recommendations are at least as similar to the recommendations the Mayo clinic returned for me as Campbell's.

That is, I can make a symmetrical argument for a significantly different diet (2), complete with experts and evidence and stuff.

So, to address your questions directly: you should believe that nutrition is a young and complex field, and therefore shouldn't have everything all figured out; my take is that you may do well to replace grains with root vegetables, since that's something everyone agrees is good (plus they're really tasty!); this isn't good enough to inform your dietary choices because I just used a symmetrical argument for a diet that has nonnegligible discrepancies with the diet Campbell recommends; and I don't know how to dig out a signal that experts, to my knowledge, haven't managed to dig out without becoming an expert.

(FWIW, I spent about 5 years as a vegetarian, followed by 1.5 years doing the paleo thing, and now subsist entirely off DIY soylent, which combines the virtues of deriving all its protein from animal sources and being processed.)

(1) Interestingly, Campbell's and Lindeberg's diets can be eaten simultaneously, and this intersection is 100% in-line with what the Mayo clinic recommended me. The difference is that Campbell allows grains and beans, and Lindeberg allows (unprocessed) lean meats, fish, and eggs.

(2) Again, there's substantial overlap, but also substantial disagreement: Lindeberg, for instance, observe the Inuit derive something like 98% of their calories from animal sources and are virtually untouched by Western disease, and concludes that very high consumption of (unprocessed) animals is perfectly fine, whereas Campbell claims that humans should eat minimal amounts of animal.