Chlorine dioxide breaks down to chlorite and chlorite is a free radical. The half life of chlorite in animals is a little over 40 hours, so it is possible to build up a concentration of free radicals in the body.
Chlorite penetrates all the organs of the body, including the brain, and it is believed that has an effect on the nervous system. For example, rats exhibit a reduced startle response when they have been exposed to chlorite. These effects take some time to manifest and are most likely dose dependent.
This has not been studied in humans, so there is no way of telling of moderate doses over a long period of time will result in similar damage as high doses over a short period of time. Extremely low doses, as in those used for water purification, don't seem to have any effect on the body as demonstrated in the Lubbers study.