These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Alternate Aesop Interpretation: It could also be said that the big lesson from the story is to simply ignore what the oracles say in the first place. As in each case it was the people involved trying to AVOID the prophecy that caused it. Oedipus' parents sending him to die, where he is instead brought to a different kingdom far away. He hears about his destiny, and fearing that it might happen, leaves what he thinks is his birth home. Frankly if anyone involved would have said, "This prophecy is silly" it probably wouldn't have happened.
Alternatively, don't kill people who cut you off in traffic.
Award Snub: This play is the most famous of all of Greek tragedy. When it was first performed, it got second place at the city Dionysia competition.
Upon the revelation that Oedipus is her son, Iocaste immediately leaves the room. A servant walks in shortly afterward to report that the queen has committed suicide. You may or may not find the abruptness of all this hilarious.
An earlier scene also has Tiresias giving his signature warning to Oedipus while falling down and flopping around on the ground as though spontaneously getting heart attacks. The Chorus has to regularly push him back up, almost to the point of playing catch with him, and the fact that he's been made to look like some tremendous ghostly bird does not help.
Nightmare Fuel: There's a video adaptation out there featuring every actor wearing a gigantic mask with terrifyingly huge, black eyes. Ancient Greek theater was actually performed this way, though.
Tear Jerker: It's already awfully sad seeing everything go to pot for Oedipus because of Fate, but perhaps the worst part is when he has to explain to his daughters how they will be viewed as disgusting aberrations all because of him.
Values Dissonance: Quite a bit. Mainly: To an ancient Greek watching this play, Oedipus would've deserved what was coming to him because of his pride. Nowadays, it just seems kinda mean spirited. There's also the fact that infanticide by exposure was actually common practice in ancient Greece.
It's also hard for the modern to accept the original murder of his father. The only thing that made it a crime was his eventual revealed identity. That Oedipus killed a man for a traffic violation, and even casually talked about it to others, means nobody cared. ...until they knew who it was.