On one hand, the character of Oedipus displays something quite amazing with respect to human beings, namely his relentless quest for the truth. He sends Creon to Delphi to discover the reason for the plague and when he finds out that Thebans are still harboring Laius' killer, he declares that he will find that person even if it involves his own house. Later in the play, as Oedipus moves closer to discovering his true identity and Jocasta tries to dissuade him from continuing with his investigation, Oedipus presses onward. Oedipus wants to find out if what the gods have said about him is true. Eventually, Oedipus discovers that the divine prediction about who he would become was true.
Whereas Oedipus' relentless pursuit of the truth is admirable, he also displays, in my opinion, one of the most unfortunate human behaviors, which is his denial of the evidence which seems obvious in linking him to the killing of Laius. We see Oedipus at his worst when he accuses Teiresias and Creon of conspiring against him. In accusing these two, Oedipus denies the validity of what the god's representative (Teiresias) has said and also denies the credibility of a family member (Creon).
Oedipus also comes off pretty badly when he meets with the old Theban shepherd later in the play. Oedipus' earlier threats against Teiresias are echoed with a threat of violence in his encounter with the old Theban shepherd. If the old man does not tell Oedipus what he wants to know, Oedipus threatens to hurt the old man.
In the end, we can admire Oedipus' relentless pursuit of divine truth, but we are saddened by the force he threatens to use which he has gained due to his political power. Oedipus' denial of wrongdoing when faced with accusation strikes me as a very natural thing. We see politicians do this all the time.