Vaccines are not a cure for a virus. Vaccines have been developed, which help prevent a person a person from becoming infected, but they do not cure someone who is already sick.
Prime Ministers are not elected to their office by the people. In parliamentary systems, prime ministers are the head of the legislative body and therefore selected by the members of that body. Such systems generally provide for a popularly elected office, like a premier or president.
Near the beginning of the episode, Dr. Quincy examines a child in the Republic of San Christos. He is anded a Littman stethoscope by the attending physician and he uses it with the earpieces backwards. It is quite awkward as the earpieces are meant to be used just the opposite so that the angle of the earpiece aligns with the anterior slant of ones ear canal. Something no regular user of the instrument would do.