Though I agree with the previous answer in part, my take is somewhat different.
I believe Oedipus' main flaw is hubris. Hubris is excessive pride that goes before a fall. It is a family trait, it seems, as Oedipus' father believed he could trick the gods and avoid his fate. Oedipus himself is blinded by his hubris, first metaphorically and then literallly. He refuses to heed warnings and proceeds as he, not the gods, sees fit. He tries to pay for his hubris by blinding himself, but I would argue that this action itself is a hubristic act. Once again, Oedipus tries to determine his own fate rather than leaving his punishment to the gods.