"it all sounds like a very dangerous job!"
Not really...but things like Chernobyl and Three Mile Island do happen...in the former massive and very dangerous radioactivity was released, some radioactive gas in the latter case...
except in particular areas of nuclear power plants, for example, there is little radiation. Workers wear "badges" that record radiation exposure and are closely monitored. When I studied around a sub critical nuclear reactor, for example, we were instructed to remove our badges when going outside...because the "radiation" even around the underwater reactor was so low that exposure to the outside sun would have recorded higher levels than were present inside the reactor building.
When working in high radiation level areas, workers are strictly limited in the time they are exposed...so there is potential danger, just like driving where mistakes have consequences.
Others work in nuclear medicine and while technicians may wear protective gloves (and badges) for handling patient doeses, the radioactive isotopes are relatively weak. I had thyroid nodules treated some years ago...I forget which iodine isotope...and within a week or two the active period of the isotope had passed (very short half life).
Here's some information on that sort of isotope and treatment from Wikipedia...
http://en.wikipedia.org/wiki/Iodine-131..
As you may know, the type of radiaton is also sigificant..alpha, beta or gamma ray exposure are not all equally serious...
I'm not sure exactly how much "hands" on work nuclear physicsts actually do with radioative material...