The Japanese are undergoing severe trauma in many ways and, cruelly, Nature may have delivered some blows below the belt. Despite being the acknowledged best in the world at designing and building nuclear power plants, Nature's wrath exceeded anything they could have anticipated. The earthquake and tsunami were the beginning of a terrible 'perfect storm' of events.
The detonations of atomic bombs over Hiroshima and Nagasaki, now nearly 70 years ago, had a curious impact on both the survivors and the rest of the world. At the time, radiation was a known mutagen, and everyone was concerned about the mutagenic effects of fallout, therapeutic radiation, and industrial exposures (as in uranium miners). The fear was that humans exposed to radiation would suffer mutations but since, according to evolutionary theory of the time, many of them would be recessive, they would be transmitted from generation to generation. In our huge societies, two carriers of the same mutation would be very unlikely to mate. But if we continued to accumulate harmful mutations, eventually there could be a very big genetic burden on society, as a frightening fraction of fetuses could be affected.
Well, that turned out not to be much of concern, for many reasons. Most directly, there was no elevated frequency of protein-coding mutations detected in studies of offspring of survivors of the bombs in Japan. This was compared to people who were unexposed in Japan, to different dose levels, and even to the Yanomami Indians of the Amazon basin (a main reason the South American studies were funded at the time).
Unfortunately, radiation didn't get a clean bill of health. Instead, about 5 years after the bombings, increased levels of leukemia were found in the Japanese survivors. And if all cancers are considered, the increase persisted for decades--essentially a life-long excess risk. This is the long tail of ionizing radiation damage.
Hopefully, the wind will carry the radiation released this week in Japan out to sea, where it will disperse and be of no concern. If it does hover over a city, those who do not experience very serious exposure will have to be followed, perhaps for the rest of their lives, in an attempt at early detection of radiation-induced tumors. To do this effectively, estimates of each individual's exposure will undoubtedly be attempted--based on where they were when, indoors or outdoors, and so on.
Radiation is a mutagen, but the type of risk depends on the type of exposure. WWII exposure in Japan was mainly a quick burst of gamma radiation passing through the body, and causing mutation in cells along its path. In the current case most of the dosage will be inhaled or on the skin. It could persist (e.g., inhaled isotopes could lodge in mucous membranes as they decayed over the years). Much of the externally deposited radiation probably won't pierce the skin, but isotopes breathed in or ingested could be a problem for exposed organ parts (like lining of the lungs). That could make detection somewhat easier as fewer tissues may be at risk, though it doesn't make the resulting disease less serious. But all of these mutations are in somatic, not germline tissues. So although this isn't of much comfort now, this probably means, again, little damage to the gametes and hence little introduction of new mutation into the Japanese gene pool.
We hope this is just a bit of speculation, and that successful control and friendly winds will blow this problem away, and leave the people of Japan safe--at least from radiation-induced disease. They already have plenty of problems to deal with.