The risks involved in plastic surgery are not a joke. That´s why you have to sign a consent form in where you agree that the surgeon won´t be responsible if something wrong happens. You will also sign an anesthetics consent form in where you acknowledge the fact that you can die with general anesthetics.
Having said that, if the hospital is good, they have an IC unit , reanimation and the doctor uses always the same team specially concerning anesthesiologists everything should go great.
After that you should consider the post-op ,which most times is not a path of roses and the patient feels frustrated as no one explains step by step how is it going to be, what he/she can expect and has no post op psychological support .
I did PR for famous plastic surgeons and I would advise to check everything before untaking a surgery as it´s not only your beauty but your health we´re talking about.