Jimmy falls in love with a banker's daughter (Situational)
The look Jimmy shares with Annabel Adams the first time he sees her makes him forget his identity as a burglar. The fact that she is a banker's daughter is an example of situational irony, as it puts Jimmy in close proximity to a safe he could easily rob if his safecracking compulsion were ever to return.
Jimmy's bag feels like it was full of gold bricks (Dramatic)
When she picks up Jimmy’s case in the bank, Annabel remarks that it "feels like it was full of gold bricks." In this instance of dramatic irony, the reader knows that the case is full of safecracking tools. Annabel is oblivious to the case's contents or Jimmy's past, and therefore doesn't understand the irony of her statement: the tools have allowed Jimmy to burgle so much money that they are likely worth more than their weight in gold.
Ben Price feigns ignorance (Situational)
The story ends in a moment of situational irony. Just as Jimmy turns himself in to Ben Price, the police officer decides not to arrest him, speaking to Jimmy as though he is in fact Ralph Spencer. Though Ben has been on Jimmy's case for a long time, he doesn't do as expected and arrest him, but rather grants Jimmy his false identity, having seen that Jimmy is a reformed man.