The first major flaw that Oedipus made known was his temper. His temper led him to kill multiple meen on his journey to Thebes, which led him to kill King Laius (his father) just like his prophecy said he would. His temper also caused him to disrespect Teiresias the prophet of the god Apollo and disrespect the gods, by saying that he didn't need them, and that he defeated the sphinx all by himself.
The second major flaw that Oedipus had was his inner-blindness.