Here is a detailed critique of the film, by Denise Minger.
In a nutshell, the documentary makers are doing a typical apples and oranges argument, and citing anecdote and non-scientifically significant "studies" from which they derive unsupported conclusions.
For example, as Ms. Minger points out, the film will frequently conflate the "American diet" with animal foods, when what is most characteristic of the "American diet" is the consumption of large amounts of processed foods, containing refined carbohydrates, and especially sugar and HFCS. The science just doesn't support the conclusions about deleterious effects of animal protein. In truth, human epidemiological studies of the harmful effects of specific foods are very difficult to do, and the history of good nutrition studies is dismal. You can't take data that totally fails to control for a wide range of variables and draw conclusions that disregard most of those variables, from that data. Doing that is quintessentially "junk science," and this is what this film does, over and over again, per Ms. Minger. A good example is the 1970s-80s MRFIT study, which was designed to test the theory that dietary cholesterol contributes to heart disease. Although the way it was written up was equivocal, and Time Magazine falsely concluded that it supported that theory, the actual statistics showed that there was no correlation between dietary cholesterol and coronary artery disease or incidence of MI (heart attacks) at all.
You will notice, though, that Denise Minger readily acknowledges that the diet being recommended is clearly better than a junk food diet, for the reason that the foods recommended are not refined carbohydrate. For example, most fruit, although it contains a lot of fructose, also contains to an extent its own antidote, i.e., fiber. (As Dr. Robert Lustig has explained in his famous lecture on the toxicity of sugar (here: Sugar: the Bitter Truth). So consuming natural plant foods is certainly healthier than a diet of french fries and ho-hos. But the science does not support the conclusion that meat and fish, or dietary fat in general, are causes of cancer and heart disease. These are conclusions based on an interesting hypothesis, but the science just isn't there, and, as Gary Taubes has shown in his books (esp. Good Calories, Bad Calories), there is plenty of evidence to the contrary.
See Peter Attia's The Eating Academy (theeatingacademy.com), where he talks about the current effort to launch NuSi (the Nutrition Science Institute) to fund and commission serious scientific research into just these questions.
As an aside, I would like to quote Dr. Attia on the subject of sensible moderation and the importance of reducing, if not eliminating entirely, sugar. (Ketosis, which is the body substituting ketone for glucose, as a result of the near total elimination of foods from which the body derives glucose, is an extreme which most people, unless they are seriously afflicted with metabolic syndrome or Type II diabetes, (i.e., severely insulin resistant) need not worry about).
Low carb is NOT an all-or-nothing proposition, but nutritional ketosis is. For most people, a gradual reduction in carbs, beginning with the worst offenders (e.g., sugar, followed by highly refined and processed grains) yields fantastic results, including fat loss, reduction in triglycerides, increase in size and maturity of HDL and reduction of LDL particles number (notice I didn’t say LDL cholesterol concentration, which is irrelevant). Ketosis, however, is a binary place to be, and certainly is not for everyone. The main caveat I give folks is this: If you continue to eat lots of sugar, you’re probably not doing yourself any favors eating much of anything, including fat. Sugar is a metabolic bully, and whatever you eat with sugar, your body will deprioritize metabolizing. In the late 1960′s John Yudkin published a study suggesting that it was pretty harmful to eat “lots” of sugar with fat (maybe even worse than just sugar alone, and certainly worse than fat alone, which causes no harm). If you’re avoiding sugars and highly refined carbs, the only thing else you need to think about is (fat-wise) is reducing your intake of omega-6 fatty acids. [From certain plant sources, primarily; i.e. many vegetable oils: use olive oil and canola oil].