Creon and Tiresias are conspiring to wrest his kingly powers from him. So, Oedipus attacks Tiresias verbally:

What spite and envy follow in your train! See, for this crown the State conferred on me. A gift, a thing I sought not, for this crown The trusty Creon, my familiar friend, Hath lain in wait to oust me and suborned This mountebank, this juggling charlatan, This tricksy beggar-priest, for gain alone Keen-eyed, but in his proper art stone-blind. Say, sirrah, hast thou ever proved thyself A prophet?

Oedipus's words above reveal his weakness of character. Instead of investigating Tiresias's claims, Oedipus resorts to ad hominem attacks against the prophet. It's obvious that Oedipus feels threatened by what he's hearing. He refuses to acknowledge any possibility of his involvement in Laius's death because his self-image is encapsulated in his kingship. Tiresias's words threaten that very kingship, so Oedipus lashes out in anger.

Later, Oedipus reacts much the same way with Creon. He accuses Creon of having put Tiresias up to accusing him of Laius's death. For his part, Creon tries to reason with Oedipus, but to no avail.

Thou art glib of tongue, but I am slow to learn Of thee; I know too well thy venomous hate.

If thou dost hold a kinsman may be wronged, And no pains follow, thou art much to seek.

When with swift strides the stealthy plotter stalks I must be quick too with my counterplot. To wait his onset passively, for him Is sure success, for me assured defeat.

From Oedipus's words above, we can see that his habit is to act swiftly and without forethought when threatened. Prior to his exchange with Creon, we see Oedipus's paranoia on full display. He finds secret meanings in Tiresias's words; every innocent phrase is fraught with a hidden insult or threat, and every motive is imbued with malice. It is Oedipus's paranoia that leads him to make poor decisions throughout the play. Here is how Creon answers him:

Now all men cry me Godspeed! wish me well, And every suitor seeks to gain my ear, If he would hope to win a grace from thee. Why should I leave the better, choose the worse? That were sheer madness, and I am not mad. No such ambition ever tempted me, Nor would I have a share in such intrigue. And if thou doubt me, first to Delphi go, There ascertain if my report was true Of the god's answer; next investigate If with the seer I plotted or conspired, And if it prove so, sentence me to death, Not by thy voice alone, but mine and thine. But O condemn me not, without appeal, On bare suspicion...

Creon lays out the rational path for Oedipus, but Oedipus rejects it. In this, Oedipus exhibits weakness of character. Can you see other ways Oedipus is less noble than he makes himself out to be? Refer to his exchanges with Jocasta to add to your answer.

In the play of Sophocles, Oedipus Rex, the king, Oedipus, is, indeed, nobly imperfect; this is quality that generates his hubris and eventual downfall.  Yet, it also is a quality of its own, separate from the arrogance of Oedipus.  For instance, in Act I when Oedipus speaks with Kreon about the "defilement," Oedipus entertains no adversary or impediment to his kingly abilities as he asks Kreon, "What trouble could prevent your hunting down the killers?" (131) And, in his confidence, he vows to "bring what is dark to light." (134)

That Oedipus entertains in self-confidence that nothing is beyond his control illustrates his imperfection. In Act II, he confidently utters a decree that "no further trouble/Will come to him [who knows Laios]" (216); and, if anyone knows the murderer, "he shall have his reward from me" (219).

Tragically, this imperfection in Oedipus leads to his hubris as in the progression of the play, he refuses to believe that anything may be beyond his control as he ignores all the signs around him and the advice of Jocasta.  Ironically, then, it is this hubris which causes his fate.

In my mind, I would look to the exchanges with Tiresias as an example of the weaknesses that Oedipus presents.  His inability to overcome his own sense of self and understand the counsel given by the prophet is one level where weakness is evident.  Yet, his tone of rebuke and scorn might reveal an entirely profound level of moral weakness.  It seems as if it is almost to a point where Oedipus' anger and sense of outrage is motivated by the fact that he might be experiencing some level of disquietude as to what the prophet is saying could actually be true.  I sense that the weakness here present is, as previously noted, a combination of hubris and anger.  Yet, I also sense that there is a weakness caused by fear of what could be true and the inability to do much about it.

In Oedipus Rex, Oedipus exhibits two great weaknesses: hubris and anger.

After Creon comes back from the Oracle, Oedipus angrily denounces him as a traitor.  After Teiresias warns Oedipus not to pursue his investigation into the murder of his father any further, Oedipus erupts against him as well:

Vile slanderer, thou blurtest forth these taunts,And think'st forsooth as seer to go scot free.

All of this shows that Oedipus suffers from hubris.  Since he is King and once freed Thebes from the plague of the Sphinx he thinks he can do it again.  His investigation into his father's murder leads to his own undoing:

O woe is me! Mehtinks unwittinglyI laid but now a dread curse on myself.

"Pride cometh before a fall" rings throughout the Oedipus trilogy.  However, Oedipus recognizes the folly of his sins and punishes himself.  In the end, he become a wise blind man like Teiresias.