What, according to Matthew Arnold, are the functions and qualifications of critic?
According to Matthew Arnold, a critic is expected to find out the best of what is currently available and making it known to the rest of the world.
"a critic may with advantage seize an occasion for trying his own conscience, and for asking himself of what real service at any given moment the practice of criticism either is or may be made to his own mind and spirit, and to the minds and spirits of others."
By exercising creativity, individuals needs to produce great works to achieve the literary objective. A critic plays a major role in ensuring that the creative individual understands that their work will be held against a higher standard. The critic ensures that the creative individual takes their time acquiring all materials they need to produce great works of art.
A critic's objective is to see the piece of work for what it really is regardless of the field it originates from and to ensure the best idea prevails. It is a critics role to guide public opinion and be a source of education with regards to literary works.
To qualify as a critic the individual needs to be a social benefactor and a moralist.
First, it should be noted that critics normally use "Dr. Arnold" to refer to Dr. Thomas Arnold, a theologian and headmaster of Rugby. Thomas Arnold was the father of Matthew Arnold, author of several important works on criticism, including "The Function of Criticism at the Present Time", the essay most relevant to your question.
Matthew Arnold saw literature and culture as having a civilizing influence on society, functioning as a sort of religion for a secular world. The role of the critic was to select from the mass of creative work "the best that is thought and said" and provide guidance to the general public concerning what to read and how to read it. For Matthew Arnold, it was through art that one could "see life steadily and see it whole."