Physical Danger
You may not be the one to do the autopsy, but if you are, be careful where you're putting that bone saw.
Ditto for those of you diagnosing cause of death as Ebola. That can be rather contagious, you know. No sense in dying for your work...with dead people. Luckily there is a plethora of protective gear to prevent the spread of nasty diseases.
Then there's the whole angry zombie/vampire/psycho rising from the dead thing. More coroners seem to die in horror movies than any other profession.