Physical Danger
Avoid these guys at all costs (source).
You work in a hospital. There are sick people and germs everywhere. So, yeah, there's the possibility of some physical danger. During surgeries and other medical procedures, the surgical team may be exposed to bodily fluids which can carry infectious diseases. Then there are those pesky airborne illnesses that are even more difficult to avoid.
Making sure that the established infection-control guidelines are carefully followed helps reduce the risk of exposure. Sometimes, additional safety measures are required for treating patients with highly contagious infections or viruses such as Ebola.
While not always as serious as contracting Ebola, you may have a problem as a surgical assistant if you have an allergic reaction to latex—the second skin for surgical teams.
Whether your reaction to it is relatively mild, or the type that will send you into anaphylactic shock, you'll need to discuss this early on, probably with the director of your surgical technology program, to determine if you'll be able to pursue this career. You want to help people, but chronic rashes aren't cool.