It is important to remember that Teiresias' role as a prophet in Greek culture is ironic but the emphasis on "seeing the truth" and the ability of even one who is blind to see what is right or "the truth" is a common theme in Greek literature. And Teiresias' role in the play is to see what others cannot and speak the truth to power.
He points out a number of acts of "blindness" on the part of Oedipus. Just after line 400, Oedipus notes that Oedipus blames his "temper, but do[es] not see the one which lives within you[Oedipus]. Instead, you are finding fault with me." This first act of blindness on the part of Oedipus is one of many that quickly lead to his downfall.
In his first long speech, he again makes references to the fact that he is blind but that Oedipus is the one who cannot see. He points out that Oedipus does not know his family, cannot see the troubles around him and that one day his eyes that see the brightness now will also be made dark, that blindness will physically afflict him the way his ignorance does at present.
And only when Oedipus too is physically blind will he be able to see the incest and disrespect and other crimes that will take him from his high position to that of a broken down old beggar disgusted with himself and his decisions in life.