Irradiated food is fine. Much safer than heat treated and probably more nutritious. Radiation works like this: The radiation source is placed in proximity to the food. The radiation in the source sterilizes the bad stuff. So long as no material from the radiation source (particulate matter, etc..) gets on the food, it is fine.

Radiation exposure does not cause the food to be "radioactive." You need a radiation source of beta or gamma radiation to actually stay on the material for it become "radioactive". It is a common hollywood misconception that objects and/or people can become radioactive by exposure alone and grow three eyes and have wierd looking children. Even persons exposed to high doses of radiation showed no higher rates of genetic damage passed onto their offspring than the general population.

As a matter of fact, a "dirty bomb" will not have enough radiation in it to really cause anyone harm. If the blast doesn't kill you, everything will be ok...The islamofacists would mainly do it for the terrorizing effects.