The Paleo diet is the healthiest way you can eat because it is the ONLY nutritional approach that works with your genetics to help you stay lean, strong and energetic! Research in biology, biochemistry, Ophthalmology, Dermatology and many other disciplines indicate it is our modern diet, full of refined foods, trans fats and sugar, that is at the root of degenerative diseases such as obesity, cancer, diabetes, heart disease, Parkinson’s, Alzheimer’s, depression and infertility. – Robb Wolf
First, I’d just like to acknowledge that I’m not a nutritionist or a healthcare professional. The opinions I share here are simply my own experiences and thoughts while trying this program. I also acknowledge that the topics of healthy eating, dieting, and illness are very personal, and what might work for me, might not work for someone else. We are all unique.
Excluding foods. The exclusion of entire categories of commonly eaten foods like whole grains and dairy requires frequent label reading in the supermarket and in restaurants. It may also increase the risk of deficiencies such as calcium, vitamin D, and B vitamins, if these nutrients are not consistently eaten from the allowed foods or a vitamin supplement. For example, there are some nondairy calcium-rich foods that are absorbed well by the body such as collard and turnip greens or canned bone-in sardines and salmon, but you would have to eat five or more servings of these greens and fish bones daily to meet recommended calcium needs. (Note that some greens like spinach that are touted to be calcium-rich also contain oxalates and phytates that bind to calcium so very little is actually absorbed.) One small, short-term intervention study of healthy participants showed a 53% decrease from baseline in calcium intake after following a Paleo diet for three weeks.  Furthermore, the exclusion of whole grains can result in reduced consumption of beneficial nutrients such as fiber and thus may increase one’s risk for diabetes and heart disease.
Chris Masterjohn has Cholesterol: Your Life Depends on It!, another web site pointing out that the war on cholesterol and the push to put people on statins is misguided. The site argues it is actually polyunsaturated fats, not saturated fats or cholesterol, that contribute to heart disease, cancer, liver damage, and aging. He also has a popular blog.
A diet high in phytic acid, which can be found in whole grains (it's in the bran) and beans like soy, is very detrimental for mineral absorption. Phytic acid strongly binds to minerals like calcium, iron, zinc and magnesium to form insoluble salts, phytates, which precipitate from the body and are not absorbed. Staffan Lindeberg has written a summary on phytic acid.
CrossFit gyms use equipment from multiple disciplines, including barbells, dumbbells, gymnastics rings, pull-up bars, jump ropes, kettlebells, medicine balls, plyo boxes, resistance bands, rowing machines, and various mats. CrossFit is focused on "constantly varied, high-intensity, functional movement," drawing on categories and exercises such as calisthenics, Olympic-style weightlifting, powerlifting, Strongman-type events, plyometrics, body weight exercises, indoor rowing, aerobic exercise, running, and swimming.