The Irony of Freddy's Excitement
Freddy walks into a diner to meet Holdaway and tell him that he is 'in' with Joe Cabot for his next job. He's so excited that he tells Holdaway to take care of the guy in Long Beach who helped get him his 'in' with Joe. Holdaway has to remind him that he is dealing with low-life criminals here, not his friends. The irony is that Freddy is so excited to have gotten this far that he doesn't keep it in the forefront of his mind that this is only the beginning. It gets more dangerous from here on out.
The Irony of No Names
Joe doesn't allow anyone to know anyone else's name. He assigns them colors instead. The irony in not having a name is that no one knows who anyone is, so when there's a rat in their midst they have nothing to go on to figure out who it could be. Being that this film came out in 1992, people were known by their reputation (not by online information); if you don't know someone's name you have little chance of knowing who they are, especially in the criminal underground.
The Irony of Acting Cool
One part of Freddy's 'Commode Story' is that he is crapping his pants with fear as he walks into the bathroom with the cops. But, by choosing to stay cool the cops don't suspect that anything is up with him. Underneath the surface he wants to sprint out of the bathroom, but on the surface he stays as cool as the other side of the pillow, thus making it out of the situation by not reacting to his fear. Though this story is fictional it also mirrors what Freddy may be feeling while he tells the story to Joe and the guys. As he looks and acts cool on the outside, but may be losing it inside.
The Irony of Mr. Blonde as the Scapegoat
When Eddie, Mr. White and Mr. Pink return to the warehouse, Mr. Orange tells them that Mr. Blonde was going to kill them all and take the diamonds for himself. The irony here is that Mr. Orange didn't count on Eddie and Mr. Blonde being so close. Mr. Blonde had just done four years in prison and didn't rat on Joe nor Eddie. So, while using the wild-man as the scapegoat seemed to be a good choice for Mr. Orange, it actually gave him away.
The Irony of Defending Mr. Orange
When Joe pulls a gun on Mr. Orange and is going to kill him for being the undercover rat, Mr. White pulls his gun on Joe, and Eddie trains his gone on Mr. White. White believes in Mr. Orange, that he's a good young kid, not a rat and is willing to kill Joe if he shoots him. After the bullets rip free from their pistols Joe and Eddie lie dead and Mr. White crawls with a bullet in him to hold Mr. Orange who confesses that he is a cop.