I know this technically isn't a biohazard, but I feel we aren't monitored as closely as we should be regarding radiation exposure. In the ER I work at, x-rays a constantly being shot and no one is issued any sort of monitoring device.
On a more biohazardy note: The ER is a particularly interesting place as far as biohazards go. We take care of lots of patients, and are in close contact with patients, that turn out to have TB, bacterial meningitis, MRSA, etc. Often times we are not even aware that these infections were present until days later. Sometimes, if I took care of a patient with a communicable disease at the end of my week, I only happen to hear about it a week later after I've potentially spread it to everyone in my household.
We also take care of patient's that spit on us, hit us, throw bodily fluids, and behave violently when starting an IV/drawing blood. Drug seekers can be some of the worst offenders, and if they're homeless IV drug users, they have all sorts of nasty infections.
It's impossible to gown up in the ER for every pt at might possibly have an infection or might throw their urinal at you or spit on you. So I'm not sure that there's anything we can do about it short of making management put their money where their mouths are and let us take care of abusive patient's by putting them out on their ass in the street.