Physical Danger
If a patient hits you, it was probably on accident because they didn't have complete control over the movements of their limbs. That's about it for physical danger. And keep an eye out when you're rushing from one patient to another, and decide to run up the stairs two-by-two.
The real dangers with this job are psychological. Seek out professional help the second your profession gets to be too much for you—before your hair starts falling out, your ears start constantly ringing, and you grind away your tooth enamel.