How explicitly does the prophet Tiresias reveal the guilt of Oedipus? Does it seem to you stupidity on the part of Oedipus or a defect in Sophocles's play that the king takes so long to recognize his guilt and to admit to it?

Instead of seeming like a mistake in the play, I feel like the vagueness and openness to interpretation makes the play work in its own special way. Tiresias makes it clear to the audience that Oedipus is guilty, and recognition dawns on the entire crowd in light of the original words of the Oracle at Delphi. Oedipus, however, is blind to this fact.
His naivete in light of these events is a very important part of the story. It encapsulates his hubris—the fatal flaw that tears him apart in the end. In his own pride, Oedipus is completely unaware of the idea of being guilty himself and instead believes that the culprit is still on the loose. Because of this, his own declarations twist him into further destruction as he decrees the punishments that the guilty party should receive.
The fact that Tiresias reveals this information in such an explicit way serves to underpin the depths to which Oedipus has sunk in his own pride. He is completely incapable of realizing the truth, even if it is explicitly stated to him. The juxtaposition of his blindness with the clarity of the truth serves the play's theme overall, revealing again how destructive Oedipus's pride is.

Both ancient and modern readers are aware that Oedipus is the culprit before reading the play, due to its role as an iconic literary work that has had a major degree of cultural influence. Oedipus himself, however, has no such advantage. The events that led to his current situation, at the time of his discussion with the prophet, were a wildly improbable set of coincidences. Not only is the actual course of events described hard to believe, but, like most people, Oedipus is reluctant to believe horrific stories about himself.
Although audiences understand the words of Tiresias, there is certainly room for Oedipus to misinterpret them. Oedipus is not portrayed as stupid at all. In fact, he is portrayed as a very intelligent man who is dedicated to the welfare of the city. That is what makes his downfall tragic. One does not feel "fear and pity" at the downfall of a villain but sympathizes with a great and good (albeit flawed) man caught up in an impossible situation. The gradual realization is part of the dramatic effect, not a flaw in the play.

In Oedipus Rex, Sophocles creates the ultimate dramatic irony by allowing the reader to understand Oedipus's true identity long before he does. The effect of this irony makes the resolution of the story all the more tragic. However, the question of Oedipus's intelligence in not believing Tiresias when he identifies him as the murderer of Laius is an interesting one. When analyzing this question, a reader must examine the conversation between Tiresias and Oedipus and Oedipus's reaction to that conversation within the context of the story as a whole.
Firstly, it is important to look at the clarity with which Tiresias addresses Oedipus. When Tiresias first enters, he is reluctant to speak, but once he does, he tells Oedipus, "You yourself are the pollution of this country" (338). Later, when questioned again, Tiresias states it all the more clearly by saying, "I say that you are the murderer whom you seek" (347). Then, when he is about to leave, Tiresias leaves him with the prophecies regarding the murderer's fate saying that he will be "A blind man / Who has his eyes now; a penniless man, who is rich now / And he will go tapping the strange earth with his staff" (439-441).
If Sophocles had not created an alternate theory that arises in Oedipus's mind following Tiresias's words, it would be much more difficult for readers to believe that Oedipus is indeed intelligent. When he hears Tiresias's accusation, he first thinks that perhaps Tiresias is simply not as skilled as people claim, but as he considers the motive behind Tiresias's words, he lands on the idea that perhaps Creon, his brother-in-law, has paid Tiresias to say these things in order to usurp the throne. Although this theory is quickly denied by Creon in the following scene, it does provide Oedipus with a fairly logical explanation. After all, if Creon did want to become king, it would make sense to blame the plague that has befallen Thebes on the current king.
Within the play, the reader is privy to enough foreshadowing from characters, both when Oedipus is on and off stage, to believe that Oedipus is the murderer early on. Yet, when thinking through the pieces of information that Oedipus has, it is logical that he tries different avenues of explanation other than the truth, simply because the true explanation is so far-fetched. Thus, although it may seem that there is a plot hole following Tiresias's entrance and exit from the play, that idea is negated by the alternate theory that Oedipus designs.