As someone who was in a situation where large volumes of DU rounds were fired (pre-Gulf War in Operation Praying Mantis), I can tell you a few interesting things about this nifty metal.
First off, if you can hold a DU round in your hand, you'll be able to tell how much heavier it is in comparison to regular lead. DU rounds are used in the US Navy Phalanx anti-missile systems, spewing 3000 rounds/minute. These bullets have a very high kinetic energy when they are fired, and they penetrate incoming missiles rather well, either detonating them or damaging their guidance systems enough so they miss the target.
They are not very radioactive in a relative sense. One idiot I knew of had snagged a live DU round and was carrying it around in his coverall packets. Alpha radiation is not strong enough to penetrate bones, but having it two inches from your testes is not what I consider a Nobel prize winning move. It just so happens that he ended up with testicular cancer less than a year later. Coincidence? Perhaps, maybe it was there already. Enough to make me wary, anyway. Any exposure to something that is radioactive or has a toxic heavy metal problem is something to be avoided by sane humans. The helicopters I worked on had a device that used a beryllium cable. Safety regulations kept you from handling it too much, and not to check for broken strands with your hands, since you could get a splinter, then get blood poisoning or cancer from it. Again, something to be avoided.
As far as the DU rounds, when they're fired off by something like the Phalanx, part of the round is subjected to very high heat and pressure. This gives off some dust, especially from the wadding and the gunsmoke cloud that bellows from the gun. While it may be harmless in relation to other carcinogenic items, it still remains a nasty, toxic and radioactive cloud of crap that you do not want near your living tissues.