The first of these main climaxes can be found inchapter 5, when Napoleon drives off Snowball in a show of force and takes over the farm. This is the critical hinge around which the entire book is structured (representing Stalin's takeover of the Soviet Union), after which Napoleon continues to strengthen his dictatorship through the use of terror and propaganda.

After this point has been reached, what is observed across the second half of the book is a growing sense of oppression hovering across the action, given Napoleon's brutality and the miserable conditions on the farm. However, this cannot properly be classified as falling action, given that Orwell is already progressing into the next part of his allegory, one that culminates in the story's second key climax, in its final chapter, with the image of the pigs walking on two legs, the sheep saying, "Four legs good, two legs better," and the Commandments replaced with the statement, "ALL ANIMALS ARE EQUAL BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS."

This scene represents the final culmination of that entire downward trajectory that had been in place ever since Napoleon's expulsion of Snowball and takeover of the farm. Across the course of the novella, the pigs systematically undermine and manipulate Animalism for their own benefit while betraying its ideals, but this is the moment they abandon it entirely. After this moment, we observe the pigs' transformation into human beings (a trend that has already been in play over the course of the story) completed in the book's closing scene, as the animals observe a gathering between the humans and the pigs and are unable to differentiate between the two.

I believe the climax (or turning point) of Animal Farm comes when they send Boxer to the glue factory. Boxer was always the voice of hope among the animals with his phrases like, "I will work harder.", and "Napoleon is always right." He was also the hardest worker, who hoped that his work would be rewarded with a pleasant retirement after a lifetime of struggle.

However, when the other animals figure out that their leaders would not only deny Boxer his earned rest, but instead profited by selling him to his death...all hope seems to be lost.

SO, the denoument (or falling action), then, is after Boxer's death when the animals resign themselves to a terrible existance under the totalitarian rule of Napoleon. They know that no matter how hard they work, that the only end for all them is death.

I would actually like to add another potential climax to the list provided in the answer above. Let us not forget the destruction of the windmill and the huge blow to the animals that this is. However, I would actually want to argue that whilst the novel features many smaller climaxes, the main climax has to be the ending, which is when there appears to be no difference between the pigs and the men. This is the true climax that the novel has been leading towards, and it is clear that this confusion marks the final development or progression of the pigs and Napoleon into the tyrannical leaders that they have become. Before this point, they are despots, yes, but their true despotism is signalled when they become indistinguishable from the very men that they have supposedly been opposing through the entire novel:

Twelve voices were shouting in anger, and they were all alike. No question, now, what had happened to the faces of the pigs. The creatures outside looked from pig to man, and from man to pig, and from pig to man again: but already it was impossible to say which was which.

The sense of terrible completion with which this ending terminates the story shows that this has to be the central climax, as both we and the animals realise the true nature of the pigs and what they have been trying to do through their "rebellion" and how they have carefully shaped it.

Animal Farm cannot be said to follow the pattern of most of the novels of its time. Since it fictionalizes the rise of Stalinism, the search for the story's "true climax" may misguide the reading. There are undoubtedly at least three startling turning points that could be viewed as climaxes. The first is Snowball's ousting by Napoleon, the second the revelation that the missing puppies have been trained to hound and kill dissenters, and the third the moment when, at the end of the book, the dispossessed animals witness the reunion between men and pigs and are unable to distinguish between them.

Each of these moments will echo differently in different readers. Much as some critics try to standardize analytical approaches and provide "the" key to interpret literary works, the last word lies with the reader. It is up to him/her to appropriate and complete the writer's work.

If you are bent on identifying what you call the "true climax", turn to your own reaction to the turning points mentioned. My feeling is that the first two pave the way for the last.   

The denouement is the final resolution of a story, the outcome of the complications, the solution to the mysteries, and/or the explanation of any secrets. It ties up the loose ends. Always look to the main conflict of the story to determine when the denouement occurs. When we know how the main conflict is resolved, we know the resolution of the whole story.

The denouement in Animal Farm is when the pigs are sitting and playing poker with the humans, finalizing their deals with one another, and the other animals look in and are unable to tell the pigs from the humans. The pigs have become just like the humans, and the humans even praise them for their control over the other animals. This is the resolution of the main conflict, the struggle between the humans and the animals.

The animals, in an attempt to better their lives, revolt against the humans and take over the farm. By the end, nothing has been accomplished because the other animals are no better off than they were under the control of humans. In fact, their revolution has made things worse for them. They work harder and have less to eat. The pigs have simply replaced the humans, and this is reflected when the other animals can't tell the difference between the two.