Concerning Sassoon's "The Hero," remember that WWI shocked the world like no other war before it.  Poison gas and airplanes were used as weapons for the first time, just to name two "advancements" in man's ability to destroy other men.  Entering the war many people still viewed war as romantic and heroic, and the major countries involved thought the war would be short and would come to a swift and decisive climax.  Trench warfare alone destroyed both of these illusions.

In "The Hero," hypocrisy concerning war is exposed in numerous ways, beginning with the opening lines:

'Jack fell as he would have wished,' the mother said,

And folded up the letter she'd read.

Jack would have wished for no such thing.  He "panicked down the trench" and "tried/to get sent home."  The mother does not face reality, but instead believes what she wants to believe.  We may or may not be able to blame her for this, but it is present never the less.  The colonel makes this illusion easy for her to believe and contributes to the process of forming it.  Furthermore:

'The Colonel writes so nicely.'

He writes the letter that apparently tells how nobly her son gave his life.  Sassoon uses irony here--the letter is written so "nicely" although it contains news so grizzly and stems from a war so brutal--to demonstrate the hypocrisy involved.  The "Brother Officer," too, tells "gallant lies" that make the mother think her boy was "brave" and "glorious."  But her boy was actually a "cold-footed, useless swine."  The letter and lies are both hypocritical, as is the mother's willingness to believe the truth about her boy and the situation he was involved in.

Finally, "no one seemed to care/Except the lonely woman with white hair."  No famous soldierly camaraderie came into play at the death of her son.  Nobody cared. 

Society's illusion-filled attitudes toward war are maintained and perpetuated by the military and the people who are gullible enough to go along with it.

I think that there are two major types of hypocrisy that the this poem is meant to expose.

First is the idea that everyone who dies in the war is a hero.  The Colonel talks about how well Jack died, and the title of the poem implies Jack is a hero.  But, in reality, Jack was an idiot and a coward who died pointlessly.

The second is the idea that the country really cares about its soldiers.  In this case, we see that no one cares about Jack's death except his mother.