At the beginning of Oedipus Rex, Oedipus demonstrates many qualities of a leader and describes himself as such. Throughout the Prologue and act I, the people of Thebes are suffering under disease resulting from a curse from the gods. Oedipus, as king, presents himself as a concerned fatherly figure by calling his subjects his "dear children" and by going to hear from them directly rather than sending someone in his place. He has also sent Creon, his brother-in-law, on behalf of his people to Delphi before his subjects even come to the palace. In conversation, he also brings up his past exploits, such as defeating the Sphinx that terrorized Thebes before Oedipus was able to answer her riddle. Thus, it is communicated to the reader that Oedipus is a strong, intelligent, and dedicated leader to his people. These qualities are all things that Oedipus mentions about himself, so the reader can also infer that Oedipus has a rather high opinion of himself, even if that opinion is justified.
In Act I, Oedipus finds that his city has been plagued by famine, fires, and other destructive acts. (One has to wonder why he is so removed from the events that he must be told that these things are happening.) Still, Oedipus seems to be a leader willing to take action and seek resolution to the plights of Thebes. He is sympathetic to his people and not so consumed by power that he will not seek help. He has sent Creon to Delphi to receive the Oracle of Apollo for guidance.
However, when the oracle is given to him, Oedipus fatal flaw is revealed: his hubris. He refuses to believe the truth that Tiresias imparts: that it is he who has killed his father and married his mother.