The effects of radiation on organisms of all kinds are very well documented.  There is a large body of peer-reviewed literature on the subject.

Perhaps this link will help you get started:
http://www.hps.org/publicinformation/ate/cat25.html

It's from the Health Physics Society.  Health physicists are usually radiobiologists who specialize in measuring radiation health effects.

Usually laypeople do not distinguish between low-dose and high dose exposure.

Everyone in the field of radiobiology agrees that the effects of low-dose radiation are extremely hard to detect.  I don't know about Swiss nuclear plants, but the estimated exposure from an American nuclear plant is .0009 millirem.  The average global exposure from natural background radiation is around 240 millirem.  So it is extremely hard to identify a single case of cancer or a mutation as being definitely caused by radiation exposure.  The only way you can tell is epidemiologically. You need a large population, like the atomic bomb survivors, and you compare their rates of ailments known to be caused by radiation exposure with those of a control population.

A lot of studies have been done of the Chernobyl area on humans and other species.  See the report of the Chernobyl Forum--a group of 11 different international agencies (WHO, etc.).  The humans who were exposed to radioactive material from the reactor accident do not exhibit higher rates of leukemia than the rest of the population, although this had been expected.  The 2,000-plus cases of thyroid cancer are attributed to radio-iodine uptake from the reactor emissions.  This could have been avoided if the Soviets had distributed potassium iodide.  In Poland, where that was done, there is no increase in thyroid cancer.  Fortunately it is a very treatable cancer.  In fact, it is treated by irradiating the thyroid.  Today the Exclusion Zone around Chernobyl has an average background radiation lower than that of parts of Spain, France, Finland, Brazil, Iran, China, and the US.  This is because the land is naturally low in uranium, radium, and thorium ore.

Nuclear medicine exposes millions of people annually to diagnostic and therapeutic radiation, sometimes very high doses to kill tumors.  Many studies have been done of the effects of these dosages.  The people I know who have undergone such treatments are happy to have had their lives extended.