What moral does the chorus see in Oedipus's life?

The transmitted text of the play ends with a brief speech by the chorus, which applies the lesson of Oedipus's life:

You residents of Thebes, our native land,look on this man, this Oedipus, the onewho understood that celebrated riddle.He was the most powerful of men.All citizens who witnessed this man’s wealthwere envious. Now what a surging tide of terrible disaster sweeps around him.So while we wait to see that final day,we cannot call a mortal being happybefore he’s passed beyond life free from pain. (trans. by Ian Johnston)

Oedipus, as great as he was, still fell into dreadful misfortune, and this is a lesson for all mortals: we ought not to consider anyone truly happy (in the sense of fortunate or blessed) until we see the end of their life, since good fortune can always be lost.
This same moral is also famously expressed in Herodotus's account of the meeting between Solon and King Croesus, where Solon several times says that he cannot call Croesus blessed until he sees how Croesus's life ends. Herodotus concludes,

It is necessary to see how the end of every affair turns out, for the god promises fortune to many people and then utterly ruins them. (trans. by A.D. Godley)

It should be noted that this final speech by the chorus is widely agreed to be inauthentic and not truly written by Sophocles.
http://johnstoniatexts.x10host.com/sophocles/oedipusthekinghtml.html

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0126%3Abook%3D1%3Achapter%3D32