Here's my take on the post from a radiation physics point of view.

I'm not convinced that these pose a great radiation risk. I would be mostly concerned about people with genetic conditions, who could not normally undergo x-rays, but then again flying itself might be worse from a radiation point of view. I'm much more concerned about the civil liberties issue.

Firstly, I'll say one thing: there is no such thing as a truly safe radiation dose.

The problem with this statement is that there is very poor data for low dose, long term exposure. And as you can imagine, it's not exactly easy to set up controlled experiments. The generally accepted model is the linear, no threshold model, which agrees with his statement. But there is some evidence for a threshold limit (below which cancer doesn't occur) and slight evidence that small amounts of radiation is actually beneficial (hormesis).

At a fundamental level, the main effect we need to be concerned with is high energy particles smashing into a piece of DNA and doing just the right amount of damage to cause the cell concerned to start doing something it shouldn't.

Actually, for photons (x-rays/gamma rays), most damage is done by so called indirect damage, where the photon creates a free radical (in this case OH.), which then interacts with DNA.

it's worth remembering that one hit that gives you cancer or leukaemia is enough to kill you. Just one. Even though most interactions won't kill you, it only takes one good one to finish you off.

This is just plain hyperbole. You almost certainly need multiple radiation interactions to produce DNA damage that will result in fatal cancer. Most DNA damage is repaired by the cell, most persistent DNA damage is benign, and most cancer is killed off by the body. That's not even to say anything about the fact that once a cancer gets to the point of discoverability that most are survivable (you still don't want cancer though!).

I remember hearing somewhere, years ago, that there is an extra component between the primary and the secondary that slows down hard X-rays to soft X-rays

This was in reference to the hydrogen bomb. You can not (generally) change the energy of x-rays. You can "harden" an x-ray beam energy distribution by filtering out the lower energy x-rays, but not the other way around. I assume he really meant neutrons.

The main mistake he (and others) makes is seeming to not understand the nature of radiation dose and how that relates to the body. Dose is simply the amount of energy deposited by radiation per unit mass. It can be thought of as a density like quantity. The related term equivalent dose is used for setting radiation exposure limits and takes into account the biological effects of different radiation types (and energies) and different tolerances of organs and tissues.

When people see that low energy radiation is mostly absorbed near the bodies surface, this seems to concern them a lot. What is more important is what the actual dose is. From a general carcinogenesis point of view, it's actually considered better that the dose is not to the entire body

What's generally not understood is that limit of dose to a specific part of the body (e.g. skin) is higher than the limit of the total body dose. This is because your body is better at dealing with localized damage, than it is with systemic damage.