What are some examples of a lack of communication in Acts I, II or III of Romeo and Juliet, preferably Act I or II.

Shakespeare uses dramatic irony throughout his play Romeo and Juliet. Dramatic irony is when the audience knows something which one or more of the characters is unaware of. Because of this, misunderstandings and lack of communication are prevalent.

The biggest lack of communication is between Romeo with his parents and Juliet with her parents. Nether is able to discuss the most important things in their lives. In fact, there is no scene in which Romeo talks with his parents. For Juliet, it is always a one way discussion with her parents basically telling her what to do and think. Romeo also lacks true communication with Mercutio and Friar Lawrence.

In Act I, Lord Montague has no idea why Romeo is acting so moody and depressed. Rather than talk to his son directly he asks Benvolio to discover Romeo's problem. Lord Montague fails to realize his son is quite the romantic and falls in love easily. It never seems to occur to Romeo to communicate with his father about the fact he has fallen in love with a Capulet.

Even though they are best friends Romeo lacks communication with Mercutio in Act I, Scene 4. Romeo has had a disturbing dream foretelling his imminent death. When he tries to tell Mercutio, his friend, always wanting to be the center of attention, launches into his Queen Mab speech, forgetting to listen to Romeo. At the close of the scene, Romeo tells the audience about his dream. In an aside he says,

I fear too early, for my mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night’s revels, and expire the term
Of a despisèd life closed in my breast
By some vile forfeit of untimely death.
But he that hath the steerage of my course
Direct my sail. On, lusty gentlemen.

The audience may assume that since Mercutio is his closest friend Romeo would discuss his private feelings with him. But Romeo never mentions Juliet to Mercutio. Maybe he is afraid because Mercutio is so committed to the feud and hates the Capulets. 

Romeo also lacks communication with Friar Lawrence. The Friar agrees to marry Romeo and Juliet because he thinks it may end the feud. He advises Romeo to take things slow and ease into his love with Juliet. He says in Act II, Scene 4, 

Wisely and slow. They stumble that run fast.

And later when he performs the marriage he reiterates his feeling that Romeo should calm down and reflect on what is happening. He fears that Romeo is rushing into something that may backfire. He says, in Act II, Scene 5,

These violent delights have violent ends
And in their triumph die, like fire and powder,
Which, as they kiss, consume. The sweetest honey
Is loathsome in his own deliciousness
And in the taste confounds the appetite.
Therefore love moderately. Long love doth so.
Too swift arrives as tardy as too slow.

Romeo, of course, never listens. He plunges into his love for Juliet without communicating with anyone in his family, and in Act III he impulsively flies into a rage when Tybalt kills Mercutio.