What claims (if any) to ignorance does Socrates make as regards himself? He emphasizes both his individual and an overall human lack of knowledge to a far greater extent in other dialogues. Why might such a focus here be absent?
Socrates professes ignorance only twice, in 506a and 509a. Moreover, these brief utterances come quite late in the discussion—a fact that, when combined with such infrequent instances, renders the point all but obsolete. This lack of focus on the elusiveness of knowledge is indeed uncharacteristic of many Platonic dialogues, several of which have as their entire purpose the study of human ignorance.
One possible explanation for this absence of skepticism about what Socrates knows lies within the turmoil of Plato's time. Amidst the Peloponnesian War, civil strife, political corruption, and the recent trial and death of Socrates, Plato must have felt strong passion for the topics of Gorgias because of their intense contemporary relevance. He therefore, through Socrates, chooses to weigh in powerfully and convincingly at the expense of his more typical hesitancy about knowledge due to the urgent problems of justice and virtue Athens (and Greece) faced at the time of the work's writing.
How does Socrates distinguish true arts from false ones (routine, flattery)? What makes something an art?
The essential distinction between true and false arts lies in that art aims at the good, while flattery aims at the pleasant. Though a full elaboration of difference between the good and the pleasant does not come until much later in the work, Socrates does provide some examples to help illustrate his point. Cookery, for instance, is NOT an art, since it creates a false impression of health and robustness through the pleasure of good eating. Medicine, however, is a true art since it aims directly at health (a good), sometimes even at the expense of something pleasant.
True art therefore denotes those pursuits that target the good, while false arts refer to those which utilize the pleasurable to create a deceptive impression of being the good.
Various opinions exist concerning what is the main topic of Gorgias: rhetoric, politics, justice, etc. Is there one underlying focus of the dialogue? If so, then what is it? Please explain your answer.
There is no one definite answer to this question, since only Plato himself knows what his aim was in writing Gorgias. Certainly one strong contender is truth, since this pursuit is an overarching theme of Plato's writings in general, in addition to being plainly stated as an ultimate goal by Socrates within the dialogue.
However, upon analysis of the discussion of each significant topic within the work, a pattern emerges. Whether considering justice, rhetoric, temperance, politics, or teaching, Socrates's statements and beliefs tend to depend upon the matter of right versus wrong within each specific arena. All value determinations are dictated by such a focus. In light of this continually recurring theme, then, the main focus appears to be human virtue and proper living.