The chief inspiration for this episode is Henri-Georges Clouzot's classic suspense thriller, The Wages of Fear (1953). Only instead of sweaty sticks of gelignite, we have nuclear weapons.
Most fuel rods used in nuclear power plants are made from uranium-235, if that is what these fuel rods for sale are made of they would contaminate an area for much longer than 1,000 years. A number of isotopes of uranium and plutonium have extremely long half-lives: plutonium-239, the primary material used in nuclear weapons, has a half-life of 24,110 years; some reactors use uranium-233 which has a half-life of 160,000 years; finally uranium-235 has one of the longest half-lives of naturally occurring radioactive isotopes coming in at 703.8 million years.
Dirty bombs have much more impact as a psychological weapon than they do as a weapon of mass destruction, in fact a dirty bomb is not technically considered to be a weapon of mass destruction. There is much misconception regarding dirty bombs, their true use is as a area-of-denial weapon, the initial blast is likely to kill a lot more people than the radioactive material it is mixed with. A test explosion, done with the elements likely to be used, and calculations done by the US Department of Energy showed that a dirty bomb detonated in a large city would expose people to high amounts of radiation, but the radiation levels would not be fatal, assuming they left the area; they would however have a much higher risk of cancer in the future. It would be extremely difficult for a terrorist group to get their hands on weapons grade nuclear material, they would most likely use industrial and medically use materials like Caesium-137, Cobalt-60, Strontium-90 or Iodine-131. These isotopes all are either alpha or beta decay, meaning they can easily be shielded against, alpha particles can't penetrate skin and beta decay particles can be stopped by an inch of plastic. So if a dirty bomb were detonated in Manhattan most people in the city would only get minimal exposure as the radiation would not penetrate inside a building, save for through the ventilation system, most of the deaths would be from the explosion itself, very few would actually die from the radioactive material, and they would just be the people in the immediate vicinity who were outside. The true damage the bomb would do is financial and psychological, that part of the city would have to be evacuated and cleaned up, which would take a few years and be extremely expensive. With proper decontamination the area would be safe to live in again within a few years, but the stigma, fear and misinformation surrounding radiation would make it far less likely for people to move back into the area.