It's difficult to predict the extent of a dirty bomb's damage because there are a huge number of variables at work. The type and quantity of the explosives and radioactive material make a big difference, of course, but completely random things like wind speed would also have an effect. There's also a lot of debate on what the long-term health effects would be.
The most likely dirty bomb would contain a small or medium amount of explosives (10 to 50 pounds [4.5 - 23 kg] of TNT, for example) with a small amount of low-level radioactive material (say a sample of cesium-137 or cobalt-60 from a university lab).
This sort of bomb wouldn't be terribly destructive. Most likely, any immediate deaths (and all property damage) would be from the explosive itself rather than the radiation. The explosive would act as a propellant force for the radioactive material. A radioactive dust cloud would extend well beyond the explosion site, possibly covering several square miles. Bombs containing radioactive waste from nuclear power plants or portable nuclear generators would inflict more damage, but terrorists would be less likely to use them because they are harder to handle. The bombers could die from exposure just building and transporting the bomb.
If people got rid of contaminated clothes, showered and evacuated the area within a day or so of a small or medium blast, they would probably be fine. The bomb would boost radiation levels above the normal, "safe" level, but not by a lot. In the short term, the human body could handle this increased exposure fairly easily. People very close to the blast could conceivably suffer radiation sickness and might require hospital care.
The main concern would be prolonged exposure. Many radioactive isotopes bind with other materials, including concrete and metal, extremely well. This would make it nearly impossible to completely remove the material without demolishing all contaminated structures. Clean-up crews could wash away a lot of the radioactive material, but a small amount would probably remain in the city for many years, even decades. Anybody living there would be exposed regularly to this radiation, which could conceivably cause cancer.
The question is, would this make a significant health difference? There are two schools of thought on this issue. Many experts have asserted that the health risks would be negligible if the government spent a few weeks or months on clean-up. The radiation level would be only marginally higher than normal, acceptable levels, and it would not significantly increase the risk of developing cancer. (See "Dirty Bombs" Much More Likely to Create Fear than Cause Cancer from the American Institute of Physics for more on this viewpoint.)
The other school of thought asserts that such an attack could make a city uninhabitable for years or decades. The Federation of American Scientists (FAS) recently prepared a report detailing three representative scenarios of a dirty bomb attack. In all three scenarios, the FAS asserts that the risk of cancer in some contaminated areas would be so high that the government would desert or demolish the area. These predictions are based on the Environmental Protection Agency's current guidelines for safe radiation levels. (Check out Dirty Bombs: Response to a Threat for the FAS' predicted scenarios.)
There's no precedent for a dirty bomb attack, but we can learn from other incidents of radioactive contamination. Nagasaki and Hiroshima were both exposed to a much larger amount of radioactive material, from an actual nuclear blast, and today, they're both considered completely safe for habitation. On the other hand, there are still areas around Chernobyl that are considered unsafe because of high radioactivity.
No matter their opinion on the long-term health risks, most experts agree that a dirty bomb would be more of a disruptive weapon than a destructive weapon. The news of radioactive contamination would probably cause widespread panic, and the rush to evacuate the targeted city could actually cause more damage than the bomb itself. A country's economy could also take a dive, especially if the bomb went off in major city. Even if the government did assure the public that the area was inhabitable, real estate values and tourism could plummet.
This is the precise reason dirty bombs are such an attractive weapon to terrorists. Their main goal is to get people's attention and inspire terror, two things a dirty bomb would certainly accomplish.
For much more information on dirty bombs, including possible scenarios for such an attack, check out the links on the next page.