The disadvantages of an absolute monarchy are many and include the absence of democratic processes, the monarch's lack of accountability, the difficulty in changing internal aspects of the government and the excess of fame that is lauded on to a single individual. The lack of democratic processes is one of the problems that many people have with an absolute monarchy because the monarch is not chosen by the people.
There is no election that yields a winner to take the "monarch" throne, but rather the monarch is selected by either noble birth or by a select few individuals who were, once again, not chosen or elected by the people. The monarch in an absolute monarchy is lauded with fame and power that cannot be broken by anyone around them. This monarch is then not held accountable for his or her judgments and can make whatever rules or judgments he or she sees fit. Moreover, it is difficult to change the internal government in an absolute monarchy and if the people want a new monarch, they have no legitimate options to replacing the existing monarch.
Today, the Vatican (often called the "Holy See") in Rome is the last "absolute monarchy" in the world. The pope, once elected, does not have to listen to any other human being while ruling the land. He has authority over the people and the Church. He also has authority over all Roman Catholic Church members in other countries as long as they are following the way of the Church as he is the absolute leader. There is no such thing as a separation of powers in this organization and in the Vatican.