It is difficult to identify ways in which Oedipus is wise in Sophocles' Oedipus Rex, mainly because Oedipus constantly fails to recognize that he himself was the killer of Laius.
Early in the play, the story of Oedipus solving the riddle of the Sphinx is recalled. Indeed, on that day, Oedipus was the wise savior of Thebes and he boasts of his wisdom on that day.
Throughout the course of Sophocles' Oedipus Rex, though, Oedipus constantly fails to recognize his true identity. He rejects Teiresias' wisdom and insanely believes that Teiresias and Creon are plotting to overthrow him. Oedipus failed to realize that Polybus and Merope were not his real parents. He failed to realize that it was he who had killed Laius, despite ample evidence to the contrary.
Perhaps Oedipus becomes truly wise once he learns the complete truth about his identity and blinds himself. His loss of physical sight perhaps marks the beginning of true wisdom as he now comes face to face with the self that the gods had told him that he was.