In literature and film, there are various stages which reveal aspects of the work being analysed in terms of its dramatic structure. This structure ensures that the story flows and reaches a satisfactory ending. The introduction or exposition when the characters, setting and basic ideas of the story are introduced helps the audience or the reader to identify with the characters and accept and understand the story. As the story progresses the rising action becomes apparent as conflicts develop and complications arise which build towards a climax. There is often tension and excitement and, in terms of A Midsummer Night's Dream, certainly confusion.  The climax is the turning point in the story and the audience or reader ponders whether the main characters will succeed in their efforts or fail. 

In A Midsummer Night's Dream, the comedic effects of Puck's mischievous magic and the resultant series of unlikely love choices, mean that things at this point could go terribly wrong. The fate of the main characters lies in Puck's hands and he has the power to correct the effects of his love potion or to watch the lovers make mistakes and continue in their bewilderment. Towards the end of Act III, scene ii Helena refers to Hermia as "little but fierce" (325) and Hermia is incredulous at the events that are unfolding and Demetrius and Lysander have resolved to fight for Helena. Therefore, this is a turning point or climax and only intervention by Puck can resolve the conflict.   

The falling action will subsequently reveal how the conflict will be resolved and the resolution will ensure that things return to normal or, in A Midsummer Night's Dream, love will prevail and will resolve all the issues ensuring that all the characters are content with the result. 

I believe that the climax of the play comes in Act III, Scene 2, when the four lovers are at the height of their confusion.  Both Demetrius and Lysander are pursuing Helena, and both Helena and Hermia are amazed at this.  The guys go off to find a place to fight, and Hermia threatens Helena with a physical fight as well.  They all run off and Puck and Oberon are left to trick them into the right areas to sort it out.  The falling action begins in IV, 1 when Theseus and the other Athenians find the lovers in the woods and the triple marriage is set.  My opinion is based on the main plot of the four lovers.  If you focus on the Titania/Bottom subplot, the climax of that story comes in IV, 1, with Titania and Bottom at the height of their infatuation.  

The climax of A Midsummer Night's Dream is act 3, scene 2. The climax is the point at which all of the tension in a story culminates—when the drama gets most intense.

In act 3, scene 2 of this play, the four human lovers, Demetrius, Helena, Lysander, and Hermia, all confront one another. Oberon’s servant Puck was supposed to put a love potion into Demetrius’ eyes so he falls in love with Helena, but he accidentally put it in Lysander’s eyes. When Oberon realizes this, he puts the potion in Demetrius’s eyes. Because of this mix-up, both Demetrius and Lysander fall in love with Helena when they wake up.

The climax comes in this scene because now, both Demetrius and Lysander are chasing Helena around and she cannot understand why. She thinks they are making fun of her and it is all a big joke. Fed up with them all, she exclaims,

O spite! O hell! I see you all are bent

To set against me for your merriment.

Meanwhile, Hermia is very upset, because she cannot believe that Lysander is being mean to her. She and Lysander are in love with one another, so his sudden change in behavior shocks her. Hermia begins to fight with Helena, and Demetrius and Lysander are on the brink of physical confrontation.

Ripe with confusion, misunderstanding, and tension, this argument between all four of the lovers is definitely the most intense scene in the play. It all gets resolved at the end of the scene when Oberon has Puck separate the men and then puts a potion in Lysander’s eyes to counteract the other one. But despite the role that magic played in this confusion, Puck still makes an insightful observation in this scene when he sees Lysander pursuing Helena and says:

Lord, what fools these mortals be!

The climax of the story is the moment of crisis and the moment of greatest emotional intensity. It is also the point at which the crisis begins to be resolved but has not yet reached full resolution.

In A Midsummer Night's Dream, the crisis takes place the moment Oberon enchants Demetrius into falling in love with Helena. At the same time, Puck brings Helena back on stage with Lysander chasing after her, so that now both men are pursuing the same woman, which happens to be the opposite woman they were pursuing at the beginning of the story.

In this scene, Puck reaches a moment of emotional intensity because he finds it hilarious that both men are now pursuing the same woman and refers to all of the Athenians as fools. Also, he says that absurd things please him best, as we see in his lines:

Then will two at once woo one.
That must needs be sport alone;
And those things do best please me
That befall preposterously. (III.ii.119-122)

Also, enchanting the lovers creates a great deal of animosity amongst the Athenian characters. Instead of being overjoyed that two men now love her instead of none, Helena distrusts their sincerity and accuses both men of mocking her. Not only that, she accuses her best friend Hermia of being in on the joke. Since the mix up of the lovers causes so much animosity, we see that this is the most emotional part of the play.

We begin to see the resolution take place when Oberon gives Puck orders to stop the fight between the two men and make them follow him all over the forest until they drop from exhaustion so that both men can be enchanted with the love flower again and this time paired with the correct woman.