The Scholar Speaking Directly to Camera (Situational Irony)
Kimball and Pacino get into an argument about the fact that Pacino has been featuring scholars speaking directly to the camera about the plays. Kimball thinks that Pacino is privileging the academics, and jokes that the theater people do not get to give authoritative interviews where they speak directly to the camera. Pacino laughs along with Kimball about this distinction, when suddenly the scene cuts to a scholar speaking directly to the camera. This editing work is an ironic wink to the audience about the fact that Pacino does give the scholars featured in the film a certain amount of authority. Then, in an even more ironic twist, the scholar interviewed expresses some feelings of uncertainty, and exposes his own lack of definitive authority.
Teenage obliviousness (Situational Irony)
Pacino is obsessed with Shakespeare's Richard III and is so enthusiastic about transmitting his passion for the project to an audience. In fact, he is so enthusiastic that he performs part of the play for a group of high schoolers in a theater, hoping that his enthusiasm will rub off on them. In an ironic contrast, the filmmakers shoot two high schoolers making out in the back row of the theater, while Pacino passionately performs the play.
Clarence's Death (Dramatic Irony)
In Shakespeare's play, Clarence is imprisoned in a tower and believes it was the Queen who has imprisoned him. Ironically, it is actually Richard who sent him to this prison, and who eventually has him killed. There is a dramatic irony in the fact that we know about Richard's evil machinations before Clarence does.
Lady Anne Scene (Dramatic Irony)
The dramatic tension of the scene between Richard III and Lady Anne is the fact that Richard is plotting to seduce her, even though she has countless reasons to be repulsed by him. As they move through the scene, Richard's manipulations actually work, and there is an ironic tension between the fact that the viewer knows Richard is up to no good and the fact that Lady Anne has no idea.