Smith doesn't know about Taylor when he is appointed (Dramatic Irony)
From the start, the viewer knows that Jim Taylor controls the political arena in Smith's home state. Hopper convinces Taylor to approve his appointment of Smith only on the grounds that Smith will not ask any questions and will be more of a stooge than a politically-minded individual. Smith has no idea that this is why he was appointed, however, and is simply honored to have been given such a large promotion. Thus there is dramatic irony in the fact that the viewer knows about the corruption of Paine and the thinking behind Smith's appointment long before he does.
Smith wins (Situational Irony)
When Smith ends up asking questions and eventually exposing the corruption of Washington, it is ironic, because he was appointed because of the unlikelihood of his doing so. Hopper makes a case for Smith's appointment by suggesting that Smith is such a bumpkin and so unversed in politics that he will go along with Paine's policies without question. Ironically enough, he puts up the biggest resistance Washington has ever seen, and it is precisely that naiveté which made him seem so unthreatening that mobilizes him to fight so hard.
Saunders helps Smith (Dramatic Irony)
When she sees that Smith could possibly fight the corruption that has so exasperated her while working in Washington, Saunders takes the opportunity to teach him the ins and outs of the system and coach him through the process of initiating a filibuster. When Smith shows up at the Senate the next day, he has been coached in how to try and save his reputation and take down Taylor, but none of his fellow senators know that Saunders was the one to help him. She coaches him from the gallery throughout.
The Bill (Situational Irony)
Smith proposes a new bill for a national boys' camp that would purchase a piece of land in his home. Ironically enough, the land that Smith is proposing to purchase is the same land that Taylor set aside for a dam-building graft scheme. Thus, without meaning to, Smith comes into conflict with Taylor, the very man whose corrupt measures need to be exposed.
