First of all, he gives an exegetical and interpretive history of the phrase "pure of heart," reminding us that its automatic association with chastity is a relatively recent development (though it goes back to some Fathers, such as Chrysostom). This history is fascinating in of itself, because it shows how the treasure of the Gospel is developed in different ages, and takes on different hues and nuances while remaining faithful at the same time. (One helpful reminder in the exegetical lesson was how Christ swept away the whole sense of religious/ritual/social purity and impurity, something that was present not only in Judaism, but is a feature of all religions. It is something that one certainly encounters all the time in India, and it makes it even more of a scandal that Indian Christianity adopted caste and has only recently tried to tackle this fundamentally non-Christian accretion.)
He then goes on to talk about hypocrisy, both in its original sense (in Greek theater, where it simply meant to act, to play a part), and also in the later sense, of someone pretending to be someone he/she is not. He shares some reflection on both religious and non-religious hypocrisy. Hypocrisy, he suggests is what is directly opposed to purity of heart. Rather than being a virtue among other virtues, then, purity of heart is "a quality that should go along with all the virtues, so that they are truly virtues and not rather 'glittering vices.'"
Here's a few things that struck me:
We have seen that in Christ's thinking, purity of heart is not opposed primarily to impurity but to hypocrisy, and hypocrisy is perhaps the most widespread human vice, and the least confessed. There are individual and collective hypocrisies.. [snip]
Man, Pascal wrote, has two lives: One is his true life and the other is his imaginary one that he lives in his own opinion or in that of other people. We work hard to embellish and conserve our imaginary being and we neglect our true being. If we have some virtue or merit, we are careful to make it known, in some way or other, so as to attach these virtues to that imaginary existence. We would rather separate them from ourselves to join them to it; and we would willingly be cowards in order to acquire the reputation of being brave. 
The tendency brought to light by Pascal has grown enormously in the present culture, dominated by the mass media, film, television and the entertainment industry in general. Descartes said: "Cogito ergo sum" (I think therefore I am); but today this tends to be substituted with "I appear therefore I am."
The worst thing that a hypocrite can do is to take himself as the standard by which to judge others, society, culture and the world. These are precisely the ones whom Jesus calls hypocrites: "Hypocrite, first take the plank from your own eye and then you will see clearly to take the speck out of your brother's eye" (Matthew 7:5).[snip]
As believers, we have to remember the saying of a Jewish rabbi who lived during the time of Christ, and according to whom, 90% of the hypocrisy of the world was found in Jerusalem. Already the martyr St. Ignatius of Antioch felt the need to admonish his brothers in faith: "It is better to be Christians without saying so than to say so without being so."
The most pernicious hypocrisy would be to hide one's own hypocrisy. I have never found in any aid to an examination of conscience such questions as: Am I a hypocrite? Am I more concerned with how other people see me than with how God sees me? At a certain point in my life I had to introduce these questions into my examination of conscience myself, and rarely was I able to pass without a problem to the questions that followed these.
One day, listening to the parable of the talents read at Mass, I suddenly understood something. Between bearing fruit with what one is given and not bearing fruit, there is a third possibility: that of bearing fruit, not for the one who has given us what we have, but for our own glory or our own interest, and this is perhaps a graver sin than bearing no fruit at all. That day at Communion I had to do as certain thieves do when they are surprised in the act and, full of shame, empty their pockets and throw what they have stolen at the feet of the owner.