On his website he has posted two criticisms, one aimed at Japan and the other at Germany (look to the right, under "Downloads and links"). His basic rationale is that since DNA can repair itself, radiation shouldn't be feared. But DNA doesn't always repair itself with 100% fidelity, that's why there is a risk of cancer from a single photon (though the risk is very, very, very low). Low doses of radiation pose a low risk of cancer, they aren't harmless.
I'll focus on the article aimed at Japan, since it's longer. I will agree with Allison, that low doses shouldn't be "feared", they should be understood. And actions should follow based on the understanding.
He says no increase in cancer death is expected in the next 50 years. Not true. We do expect an increase as a result of releasing more carcinogens (radioactivity) into the environment. Whether or not an epidemiological study can discern the increase is a separate issue. That will depend on the number of people exposed to excess doses and whether there is an attempt to locate and study them for 50 years.
He thinks the Earth formed 6 billion years ago. Not true. Our best estimate is 4.5 billion years ago.
His Figure 1 graph is simply made-up. A single photon can ionize DNA, and that damage may not be repaired.
His Figure 2 has to do with tumors, which are targeted in radiotherapy, while nearby tissues are avoided. Since there is immediate danger from the tumor, we accept a long term risk of additional cancer in undergoing the radiotherapy. This has nothing to do with radioactivity from a nuclear plant accident, which only provides cancer risk (though the nuclear plant offsets other risks from other energy sources or from a lack of energy).
He seems to think that because some people get out in the Sun, that the the UV radiation doesn't cause skin cancer. It does. It also promotes Vitamin D production. We understand this, and don't fear it. Similarly, we should understand man-made radioactivity, and not fear it at low levels. But in doing so, one shouldn't think it doesn't contribute to cancer.
I really had a laugh at this paragraph:
"Damage to DNA that is not repaired or suppressed by the immune system can lead to cancerous growth. Typically this appears later in life, when the immune system is less effective. Radiation is only a minor additional cause of cancer and its contribution can only be distinguished statistically. For example, it was responsible for an increase of 5% cancer deaths among the survivors of Hiroshima and Nagasaki who died between 1950 and 2000. The other 95% of cancer deaths were not related to radiation."
The immune system DOES NOT repair or suppress DNA damage. That is done by groups of proteins within a cell. The immune system consists of organs and cells which seek out foreign invaders to the body. If a cell's DNA is damaged by radiation it may appear foreign to the immune system, and the immune system may try to kill it. But that is different than "repairing or suppressing DNA damage".
We don't know that radiation is "only a minor additional cause of cancer". Almost half of the citizens of the U.S. will get cancer. What carcinogen are they most ubiquitously exposed to? Radiation. It's everywhere. We really don't know how cancer incidence would change if the radiation were to disappear.
His statistics (the 5%) are bogus. First, we actually measure incidence not mortality, because we don't want people to get cancer even if some can get cured. It's a scary, expensive disease. Typically, mortality is about 1/2 of incidence, though it varies by cancer. For the a-bomb survivors, the incidence was about 11% for solid cancers. I'm guessing Allison got his 5% death rate from that. Of course, these survivors received a range of excess doses.
However, this isn't really a measure of actual excess dose associated with actual site-specific cancers. If you look at the graph, it is a "weighted colon dose" meant to represent the dose associated with all "solid cancers". It is a sort of surrogate for looking at actual site-specific risks. Actual risks of site-specific cancers vary from the surrogate.
And when we look at leukemia, the risk is around 46%, or about 23% mortality.
To say that the other 95% of cancer deaths were not related to radiation, isn't true. Some of those deaths were due to background radiation. We just can't slice and dice and determine which were and which were not.