In Antigone, Creon's tragic flaw is his hubris which is exhibited in his refusal to listen to anyone's advice regarding the punishment he doles on Antigone. Creon's tragic flaw is best seen in his interaction with Tieresias. Creon admits at the beginning of the conversation that he always respects the word of Tieresias, but as the conversation unfolds and Tieresias tells Creon that he should listen to the people of Thebes and spare Antigone, Creon quickly changes sides. Tieresias says "that to err from the right path is common to mankind," but Creon does not believe that he has made the wrong decision. Creon tells Tieresias that he thinks the old man was paid to say these things to him--Creon does not believe that Tieresias is telling him the truth. Creon is too proud as the new king to admit that he may have made a mistake, and he does not want to be seen as a coward in the eyes of the people of Thebes.
The many flaws in Creon's character are all related to his willful disregard of the Greek sense of the "higher order" that governs proper behavior.
Creon's hubris is tied directly to his stubborn and short-sighted insistence that the concerns of the king and the concerns of the state are of greater importance than the concerns of the gods. In this way, Creon puts himself above the gods, overturning the natural order - the higher order - that gives structure to life (according to the philosophy at work in the play).
One way to understand the major themes of the play and Creon's role within the play is to look at the two types of morality that are in conflict in Antigone. Creon defines one morality as being aligned with the integrity of the state and its laws. (Burying Polyneices and/or allowing his burial is immoral because it will undermine the laws of the state and so weaken the social order.) Antigone defines another morality as being aligned with the will of the gods. (She must bury her brother, no matter what the state says, because this is the only moral thing to do. Burying Polyneices is the only way to maintain the integrity of a natural order that puts the gods above mankind.)
This theme of laws in conflict is conveyed as a subtle question at the end of Scene I, as the chorus speaks.
"O fate of man, working both good and evil!
When the laws are kept, how proudly his city stands!
When the laws are broken, what of his city then?"
The question becomes then which laws are to be kept? Which laws are most important? Whose morality is the "true" morality - that of Antigone or that of Creon? The fact that Creon seems to revere himself in his position of king fuels the outrage that he represents; a man fearful of his position sets himself above the gods who are quite secure in theirs. This is the folly that Tiresias tries to warn Creon about, but Creon is blind to all warnings.
Ultimately, Antigone is on the side of the true morality of the play. She is on the side of the gods. Creon's tragic flaw is his unwillingness to yield to Antigone's virtue. He refuses to even see her virtue and refuses to accept the honest assessment of the situation that Tiresias gives him.
"His refusal to bend to the will of the gods effectively ruins his life" (eNotes).
Seen in this light, Creon's tragic flaw is displayed every time he defends his decision, whether he is speaking to the sentry, Antigone or Tiresias. The chorus speaks clearly of this flaw in Ode II.
"What mortal arrogance
Transcends the will of Zeus?"