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 unwittingly
I 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.
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.