Gallimard's affair (Dramatic Irony)
Gallimard's affair with Song is an instance of dramatic irony, in that while the audience knows about it, he lies to his wife Helga, keeping it a secret. In these moments, the audience knows something that Helga does not know, and the affair carries on for many years.
Chin does not know the nature of Gallimard and Song's relationship (Dramatic Irony)
While Chin knows that Song is pretending to be a woman to seduce Gallimard and tease information out of him, she does not know that Song is having an affair with Gallimard. In one of their early meetings, Chin says to Song, "Don't forget there is no homosexuality in China!" as a way of reminding Song not to sleep with Gallimard. The audience knows that Song has been sleeping with Gallimard for a while, and that what they are doing constitutes homosexual acts, but Song keeps it a secret from Chin.
Song is a man and a spy (Dramatic Irony)
The most central dramatic irony, on which the entire plot hinges, is the fact that Gallimard has no idea that Song is not a woman, but a man in a costume. He remains in the dark for many years, and even when he knows the truth, he cannot bring himself to fully accept the fact that he has been having an affair with a man. In the moments after Song's status as a male spy is revealed and before Gallimard learns this, the dramatic irony is most potent, in that the audience knows the truth, while Gallimard is wrapped up in an illusion.
Gallimard's laughter (Situational Irony)
In a dramatic flourish, towards the end of the play, Song removes his costume to reveal his naked body and show Gallimard once and for all that he is a man. Gallimard seems horrified by the display, protesting loudly. In the moments that follow Song removing his final piece of clothing, the stage directions say, "Slowly, we and Song come to the realization that what we had thought to be Gallimard's sobbing is actually his laughter." This is a massive shift from our expectation of his response. Rather than be horrified and upset, he is struck by the absurdity of it all, laughing in a state of almost-denial about the shamefulness of his affair.
