1) A lot of discussion of being sore. Sure one of the first things mentioned is "I've been sore before", but then we move on to more complaining about it. That is a natural part of doing any new movements, no matter how in shape you are overall.
2) No appreciation of the value of high rep movements. True, they are not good for hypertrophy (probably, even there the research is shakey whether low and high should be mixed), but they are good for building connective tissue strength, for burning calories, for increasing range of motion in a movement, for bone density...
3) Author links a balanced WebMD article but the link text implies it fully agrees with the negativity.
4) Article doesn't talk much about joint issues which are probably the biggest concern a lot people have with crossfit movements. The violence of many of the movement can lead to muscle and connective tissue problems, but those heal and are obvious.
So, what are my issues with Crossfit?
1) Quality control. The excuse of crossfitters to "just find a better gym, they aren't all like that" is inadequate. Its a single program and a single franchise making money off each gym-goer, not an abstract concept like say HIIT. Ask Krispy Kreme or Quiznos how the no-quality control franchise theory works.
2) They rely on joint stability and momentum as much or more than on muscle. You are simply getting no benefit from that.
3) The movements are violent unnecessarily, this I agree with the author on. The joint reliance, the tugging at muscles and tendons, are all high risk for injury. While there are things that type of work can build that regular weight training cannot, the risk/reward is only worth it for people with specific training needs and doing specifically valuable movements. Kettle bells and kipping pull ups are pretty much never as valuable as good mornings, dead lifts, assisted pullups, and lat pulldowns. Clean and jerk has valuable movements taken separately, but combines them with high joint risk moves in between.