The biggest irony of this Act is the way in which there is a gap between the knowledge of the two principal actors and the audience in knowing that Romeo and Juliet are now married and the rest of the characters, who carry on believing that they are not married and show every evidence of still being dominated by the feud between these two noble houses. Let us just take one example to demonstrate what I am talking about.
In Act III scene 5, Lady Capulet interprets Juliet's sadness at just having left Romeo as continued grief over the death of her cousin, Tybalt. This is one example of irony, as we know that actually Juliet is sad about the way that Romeo has had to leave her for his exile. This irony continues, however, as Lady Capulet refers to Romeo in the following way:
Well, girl, thou weep'st not somuch for his death
As that the villain lives which slaughtered him.
Lady Capulet goes on to say that Juliet is weeping for Romeo because he is still alive and has not faced punishment, but there is tremendous irony in what she says, because, actually, she is right. Juliet does weep for Romeo, though not for the reasons that Lady Capulet believes at all. Such irony dominates this act. See if you can find other examples yourself now.
There are examples of situational, dramatic, and verbal irony in Act III.
In the first scene of Act III, we witness situational irony when Mercutio teases Benvolio and counsels him not to start a fight (something Benvolio has not really done)—but then himself starts a quarrel with Tybalt immediately after.
Come, come, thou art as hot a Jack in thy mood as any in Italy, and as soon moved to be moody, and as soon moody to be moved. (3.1.12-13)
Also in Scene 1 there is an example of verbal irony as Mercutio tells Benvolio that his fatal wound is but a scratch when he really knows this wound is a mortal one because he quickly asks for a surgeon:
Ay, ay, a scratch, a scratch...
Where is my page? Go, villain, fetch a surgeon. (3.1.61-62)
In an example of dramatic irony, Juliet appears to be agreeing with her mother, who wants to send someone to Mantua to poison Romeo (who has just killed Tybalt)—but really, unbeknownst to her mother, she expresses her true feelings:
Oh, how my heart abhorsTo hear him named, and cannot come to him.To wreak the love I bore my cousinUpon his body that slaughtered him! (3.5.99-102)