As long as the DU is not allowed into the environment (i.e. in a fire or crash) it is perfectly safe. Even if it is allowed into the environment, the effects of it are controversial as it is only very weakly radioactive. I think the emissions are mostly alpha particles and very, very low gamma rays, so you would need to ingest it for it to be dangerous.
It is used because its density is much, much higher than lead (by about 70% I think).