Arthur's Kills (Dramatic Irony)
Up until his murder of Murray Franklin, Arthur is an unknown murderer. With no witnesses on the train in which he killed the three businessmen, Arthur is able to continue with his life without persecution. Then, when he kills his mother by smothering her with a pillow at the hospital, no one knows it was a murder, instead believing that she died from her illness. In both of these instances, the viewer knows something that other characters do not, which creates dramatic irony.
Sophie (Situational Irony)
Throughout the first half of the film, we see Arthur developing a relationship with Sophie, the girl who lives down the hall. He kisses her passionately one night, she goes to his comedy show and laughs, they go on a date afterward, and she accompanies him to the hospital when his mother has a stroke. However, later on in the film, Arthur goes to her apartment and lets himself in, and we realize that they never had a relationship at all. Their relationship was all a delusion, made up in his head. This reversal creates an instance of irony in which the audience realizes that Arthur has been an "unreliable narrator" and all the previous scenes of their relationship have been a complete fantasy.
Penny's Delusions (Situational Irony)
Another instance of irony that hinges on delusion is the fact that Arthur's mother, Penny, is revealed to have completely imagined her relationship with Thomas Wayne and suffered from other delusions that made her a completely unfit mother to Arthur. While Arthur has maintained that she is a good, if obsessive, mother, he learns that she was institutionalized for psychosis and delusions, that she lied to him about him being adopted, and that she was complicit in his abuse as a child. This is a disturbing and ironic reversal, in which Arthur realizes that the only person he thought he could trust was completely untrustworthy.
Everyone on the Train is a Clown (Situational and Dramatic Irony)
Two detectives chase Arthur, who is in a full clown getup, onto a crowded subway car. Ironically enough, the car is filled with people dressed as clowns who have joined the movement that Arthur's violent act began. Because of this, the detectives cannot find Arthur. This is not only an instance of situational irony, but of dramatic irony, because the viewer knows where Arthur is, but the authorities cannot pick him out of the crowd.
