Many of the female surgeons will wear jewelry while scrubbing in, as well as while operating. This is prohibited in real Operating Rooms. Also, many of the surgeons (especially Dr. Maggie Pierce -Kelly McCreary) have long nails which is a no-no for a surgeon.
Throughout the series, the Chief of Surgery is shown as running the hospital and surgeons are depicted as making diagnoses. In reality, the Hospital would be run by the Chief Administrator, with a Chief of Medicine and a Chief of Surgery reporting to them. Diagnosis would be handled by medical doctors who would refer the patient for surgery.
The heads of surgical departments and attending surgeons are portrayed as middle class income earners who carpool and rent living spaces. Surgeons are generally one of the highest paid professions in the USA.