You're hanging around a lot of sick people, so depending on the contagion factor, you're dealing with some risk of getting sick. But since anesthesiologists don't physically rummage around the innards of patients like surgeons do, there's less risk of infection.
And, not to point any fingers, anesthesiologists handle a lot of powerful, psychotropic painkillers; the very same drugs have a recreational component. To some, the temptation to dip into the medical stash may prove irresistible. But then, let's hope not.