himself and a possible future wife.  Graciously, Capulet enters into this conversation quite calmly.  He doesn't say "no" to Paris marryingJuliet; however, Capulet also doesn't say "yes."  Capulet tells Paris that Juliet is still too young.  He should wait until Juliet is fifteen.  

My child is yet a stranger in the world;
She hath not seen the change of fourteen years,
Let two more summers wither in their pride,
Ere we may think her ripe to be a bride.

Capulet also says something very important.  He says that his consent to Paris isn’t the only requirement for this proposed marriage.  He tells Paris that Paris must win Juliet’s heart.  

But woo her, gentle Paris, get her heart,
My will to her consent is but a part;
An she agree, within her scope of choice
Lies my consent and fair according voice.

That is important because it shows that Capulet cares about Juliet’s happiness.  He has every right to arrange a marriage for Juliet whether she likes it or not.  Capulet is basically admitting that he believes that love (or at least liking) is necessary for a happy marriage.  A bit later in the play, Capulet will pull a complete 180 and demand that Juliet marry Paris a few days later.  

Capulet then slightly changes the subject.  He tells Paris that he is throwing a big party at his house that night, and Capulet would like Paris to be there. Next, Capulet hands the invitation list to a nearby servant, he and Paris exit, and the servant is supposed to go tell everybody on the list about the party.  Unfortunately, the servant can’t read.  

Romeo and Benvolio enter the scene, and Romeo is still whining about lost love.  The servant asks if either of them can read.  Romeo takes the invite, asks what it is, and discovers that his dear Rosaline will be at the party.  Benvolio and Romeo decide to crash the party.  Romeo wants to go to see Rosaline, and Benvolio wants to go in order to show Romeo that there are plenty of way more attractive women to woo than Rosaline.

Go thither; and, with unattainted eye,
Compare her face with some that I shall show,
And I will make thee think thy swan a crow.

Act III, scene iv of Romeo and Juliet can be argued to be the turning point of the play because this is when Juliet's father decides to rush her into a marriage with Paris within a couple of days. Juliet was safer when her father told Paris, "Let two more summers wither in their pride,/ Ere we may think her ripe to be a bride"(I.ii.10-11). But after Romeo kills Tybalt in the previous scene, Lord Capulet believes that a marriage would cheer his daughter up from mourning her cousin. Little does Lord Capulet know that Juliet is already married and this marriage to Paris will put more pressure on her than she's already experiencing with Tybalt's death and Romeo's subsequent banishment. Had Lord Capulet not forced a quick marriage on his daughter, she would have had more time to wait for Father Lawrence to work his magic in Romeo's name to bring him back. Sadly, with the pressure of a second marriage on top of a first, Juliet panics and threatens to kill herself unless Friar Lawrence figures something out quickly. Hence, act III, scene iv could very well be considered the turning point in the play.

Act 4 is the turning point of the play. Romeo has been exiled for killing Tybalt. Juliet's parents still want her to marry Paris. Juliet is in deep mourning for Romeo.

Act 4 begins with Paris coming to see Friar Laurence. He talks about his upcoming wedding. Friar Laurence, aware of the marriage between Romeo and Juliet, tries to tell Paris to slow things down. Juliet enters and after Paris leaves, she tells Friar Laurence that she would rather kill herself than marry Paris. Friar Laurence tells her he knows how she can do this. He tells her to drink a vial that he has and she will fall into a deep sleep. To the outside it will look like she is dead, but in reality she will only be sleeping. Friar Laurence tells her he will let Romeo know.

"And this borrowed likeness of shrunk death thou shalt continue two-and-forty hours and then awake as from a pleasant sleep."

Juliet goes home and her parent and nurse are all talking and planning the wedding. Juliet tells her father that she is happy to be marrying Paris. Her father is so happy that he decides to move the wedding up a day. Juliet and her nurse go the her chamber for her to get ready for bed. Juliet tells her nurse that she would like to sleep alone that night. The nurse agrees and leaves her. Juliet drinks the vial.

"Farewell! God knows when we shall meet again. I have a faint cold thrill through my veins that almost freezes up the heart of life. I'll call them back again to comfort me...My dismal scene I need must act alone. Come, vial."

The next morning, Lord Capulet is busy with the wedding plans. He tells the nurse to go and wake Juliet. The nurse tries to wake her, and when she can't she alerts the house. The nurse believes Juliet is dead. Lord and Lady Capulet and Paris all arrive and learn that Juliet has died. Friar Laurence arrives and tells them to make the wedding decorations into funeral decorations. 

The act is the turning point for everything. Friar Laurence has done what he thinks was the right thing to do. Instead of having to marry a man she doesn't love, Juliet would rather die. Friar Laurence helps her deceive everyone. The real tragedy has now been set in motion. This is such a tragic play. If Romeo and Juliet's parents had just let them be together, the tragedy would never have happened, but instead they both let past hurts dictate their actions and it cost them the most important thing to them, their children.

The plot developments listed by the other educator are probably the most important in the play, but there are others that are significant as well.

A very important plot development arises from the street fight that breaks out between the Capulets and Montagues at the beginning of the play. This is a final straw for Prince Escalus, who becomes so irritated with the endless fighting that he decrees the death penalty for those who street brawl in the future. This leads directly to Romeo's banishment when he kills Tybalt.

The marriage between Romeo and Juliet is another important plot development. They marry soon after falling in love. They marry in secret, as their families would most certainly not approve the marriage. This, however, makes it all the more imperative that Juliet not marry Paris, as otherwise she would be engaged in bigamy.

A third fateful plot twist is when Romeo misses the messenger sent to tell him that Juliet is only feigning death. Had he known his, he would not have killed himself.

Without knowing which excerpt you are referring to, I would say three of the biggest plot developments are:

* Romeo and Juliet meet at her family's party and they kiss and fall in love.  This leads Juliet to see if Romeo's intentions are true, which they are, so they get married.

* Tybalt tries to start a fight with Romeo.  Romeo being newly married to Tybalt's cousin, tries to avoid it.  Mercutio fights in his stead and is killed, Romeo kills Tybalt and then is banished.

* Juliet is supposed to marry Paris, so she pretends to be poisoned which makes Romeo think she's actually dead so he kills Paris and then kills himself.  Juliet wakes up, sees him dead, and then kills herself.