tl;dr, with my own interpretation of the article: "although we are not students in today's world, we presume to know and understand the mind of today's student and can tell you from our own learned perspective that Khan just doesn't have what it takes to teach." I'm certain I read nothing more than snobbery in this article. It reads like "we didn't think of this free online disruptive academy first" or "how dare you…
One of the authors is a current teacher, working with real students. He gets feedback from them either directly (by questions, comments, curses) or indirectly (homework, tests, quizzes) to gauge his effectiveness as an educator. Khan (until they added problems to the site) didn't have this feedback.
Their criticism boils down to a few main points.
1. He uses an inconsistent presentation of algebra and arithmetic work and notation, which could lead to students becoming confused when he suddenly changes it.
2. He uses a poor selection of examples, without offering more or better examples students may develop a mathematical toolset based on a flawed understanding, which will lead to problems further down the line.
3. The problems available to students are insufficient to provide proper mathematical practice and ensure that some of the common misunderstandings are shown to be wrong.