Dodge's whiskey (Dramatic Irony)
The first instance of irony we encounter in the play is Dodge's hidden whiskey habit. While Halie calls to him from the upstairs, urging him to take his pills, Dodge takes out a flask and takes some big swigs of whiskey. He keeps his drinking secret from his wife, who does not approve, but the audience can see him transgress.
Tilden is at Dodge's and he doesn't recognize Vince (Situational Irony)
Two instances of situational irony occur when Vince and Shelly arrive at the house. First of all, they think they are on their way to New Mexico to see Tilden, but are surprised when they find him at Dodge and Halie's house. Not only that, but in a bizarre twist, Tilden does not even recognize Vince, his own son.
Tilden's Account of the Buried Child (Dramatic Irony)
After Vince leaves to go get Dodge a new bottle of whiskey, Shelly finds herself alone with Dodge and Tilden. Tilden, who somehow trusts Shelly, tells her the story of the buried child. In this we learn the family secret and so does Shelly, but Vince isn't around to hear it. Thus, the audience and Shelly know something about Vince's family that he does not, which creates dramatic irony.
Dodge is dead (Dramatic Irony)
At the end of the play, Dodge dies, but Halie calls down to him without knowing that he has passed away. Because she is used to talking to him from the other room, she goes on a long rant about the vegetables growing outside. Meanwhile, we can see that he is dead on the couch.