Gurney Halleck wants revenge against Jessica, but the real betrayer was Dr. Yueh (Dramatic Irony)
Gurney Halleck truly believes that Jessica is the one who betrayed House Atreides to the Harkonnens. When he learns that she's alive, he vows to stop her, and he even attacks her and holds her at knifepoint in front of Paul. In this example of dramatic irony, the reader knows what Halleck doesn't: Dr. Yueh is the one who betrayed House Atreides, not Jessica, and Halleck's violence is misdirected and actually puts him in danger.
Feyd-Rautha is defeated by Paul not cheating (Situational Irony)
Feyd's one-on-one duel with Paul is narrated primarily from Paul's limited third-person perspective, so the reader knows that Paul could say a word that will immobilize Feyd but chooses not to do so. Instead he says "I will not say it!" which surprises Feyd and has basically the same effect, making him hesitate, allowing Paul to gain the upper hand. In not using his advantage, Paul gains the advantage.
This situational irony contrasts with the scene of Feyd's other one-on-one combat, his rigged slave-gladiator fight, where he uses a similar code word to unfairly kill an Atreides man.
The Bene Gesserits' distrust makes the Kwisatz Haderach useless to them (Situational Irony)
The Bene Gesserit sisterhood has tried to produce the Kwisatz Haderach for 90 generations, so that they can further their understanding of the future. However, when Jessica produces a son who might be the Kwisatz Haderach, the Bene Gesserit are angry with her for operating outside their plans. Because they're angry and cruel to Paul, treating him like a child they can control, Paul develops an intense mistrust of Bene Gesserit sisters (including his own mother at times). If the Bene Gesserit had supported Paul instead of trying to manipulate him, they might have had a Kwisatz Haderach they could control; instead, their treatment makes Paul useless to them.
In trying to destroy House Atreides, the Emperor makes Paul Atreides stronger (Situational Irony)
The Padishah Emperor supports the Harkonnen attack on House Atreides, even sending legions of his Sardaukar, largely because Duke Leto's fighting forces are getting strong enough to rival his own. However, in trying to destroy the Atreides forces, the Emperor indirectly sends Paul to the Fremen, providing Paul with an enormous well-trained army and direct control of melange.
