Bianca's Latin Tutor
Lucentio's disguise as Bianca's Latin tutor is an example of dramatic irony, because his disguise places him in the position to woo Bianca. The audience, of course, knows Lucentio's plan, and is privy to his machinations while other characters are left unaware.
Kate's Marriage
Most characters perceive Kate as a repulsive and difficult woman with a complete disdain for marriage. Indeed, Kate's headstrong behavior and vocal personality support the claim that she is not interested in getting married. It is her rebellious nature, however, that leads Baptista to force Kate into a marriage even more aggressively.
Petruchio's Claim
Early on in the play, Petruchio announces that Kate loved him so fervently that she hung around his neck and kissed him while confessing her feelings. The audience, of course, knows that Kate did no such thing, and that she in fact approached Petruchio with insults and disdain.
Kate's Transformation
For years, critics have debated whether Kate's transformation is a genuine one, a performance, or a mixture of both. As such, the "taming" of Kate is itself a form of irony, as it is left open-ended as to whether Kate has truly been transformed in to the obedient and doting wife or whether she is simply playing another role. The play, then, ultimately questions the relationship between performance and reality, a meta-theatrical question to pose as audiences watched the actors on the stage.
