The section of the text that's getting the most attention is his powerful denouncement of our current financial system, the obsession with consumption, inequality, and the tyranny of capitalism.
The key part of the text is below, though first here a few lines that really stand out.
On the importance of remembering those who are less fortunate: "We can only praise the steps being taken to improve people’s welfare in areas such as health care, education and communications. At the same time we have to remember that the majority of our contemporaries are barely living from day to day, with dire consequences."
On the seriousness of economic exclusion: "Just as the commandment 'Thou shalt not kill' sets a clear limit in order to safeguard the value of human life, today we also have to say 'thou shalt not' to an economy of exclusion and inequality. Such an economy kills."
On the failure of traditional economic dogmas:  "... some people continue to defend trickle-down theories which assume that economic growth, encouraged by a free market, will inevitably succeed in bringing about greater justice and inclusiveness in the world. This opinion, which has never been confirmed by the facts, expresses a crude and naïve trust in the goodness of those wielding economic power and in the sacralized workings of the prevailing economic system. Meanwhile, the excluded are still waiting." 
On exploding inequality: "While the earnings of a minority are growing exponentially, so too is the gap separating the majority from the prosperity enjoyed by those happy few."
On the world's obsession with money: "We have created new idols. The worship of the ancient golden calf (cf. Ex 32:1-35) has returned in a new and ruthless guise in the idolatry of money and the dictatorship of an impersonal economy lacking a truly human purpose." 
On the dangerous mix of inequality and consumerism: "It is evident that unbridled consumerism combined with inequality proves doubly damaging to the social fabric."
On the role of the state in providing for the common good and regulating the economy: "This imbalance is the result of ideologies which defend the absolute autonomy of the marketplace and financial speculation. Consequently, they reject the right of states, charged with vigilance for the common good, to exercise any form of control. "
Here's the whole section:
I. SOME CHALLENGES OF TODAY’S WORLD
52. In our time humanity is experiencing a turning-point in its history, as we can see from the advances being made in so many fields. We can only praise the steps being taken to improve people’s welfare in areas such as health care, education and communications. At the same time we have to remember that the majority of our contemporaries are barely living from day to day, with dire consequences. A number of diseases are spreading. The hearts of many people are gripped by fear and desperation, even in the so-called rich countries. The joy of living frequently fades, lack of respect for others and violence are on the rise, and inequality is increasingly evident. It is a struggle to live and, often, to live with precious little dignity. This epochal change has been set in motion by the enormous qualitative, quantitative, rapid and cumulative advances occurring in the sciences and in technology, and by their instant application in different areas of nature and of life. We are in an age of knowledge and information, which has led to new and often anonymous kinds of power.
No to an economy of exclusion
53. Just as the commandment “Thou shalt not kill” sets a clear limit in order to safeguard the value of human life, today we also have to say “thou shalt not” to an economy of exclusion and inequality. Such an economy kills. How can it be that it is not a news item when an elderly homeless person dies of exposure, but it is news when the stock market loses two points? This is a case of exclusion. Can we continue to stand by when food is thrown away while people are starving? This is a case of inequality. Today everything comes under the laws of competition and the survival of the fittest, where the powerful feed upon the powerless. As a consequence, masses of people find themselves excluded and marginalized: without work, without possibilities, without any means of escape.
Human beings are themselves considered consumer goods to be used and then discarded. We have created a “disposable” culture which is now spreading. It is no longer simply about exploitation and oppression, but something new. Exclusion ultimately has to do with what it means to be a part of the society in which we live; those excluded are no longer society’s underside or its fringes or its disenfranchised – they are no longer even a part of it. The excluded are not the “exploited” but the outcast, the “leftovers”.
54. In this context, some people continue to defend trickle-down theories which assume that economic growth, encouraged by a free market, will inevitably succeed in bringing about greater justice and inclusiveness in the world. This opinion, which has never been confirmed by the facts, expresses a crude and naïve trust in the goodness of those wielding economic power and in the sacralized workings of the prevailing economic system. Meanwhile, the excluded are still waiting. To sustain a lifestyle which excludes others, or to sustain enthusiasm for that selfish ideal, a globalization of indifference has developed. Almost without being aware of it, we end up being incapable of feeling compassion at the outcry of the poor, weeping for other people’s pain, and feeling a need to help them, as though all this were someone else’s responsibility and not our own. The culture of prosperity deadens us; we are thrilled if the market offers us something new to purchase; and in the meantime all those lives stunted for lack of opportunity seem a mere spectacle; they fail to move us.
No to the new idolatry of money
55. One cause of this situation is found in our relationship with money, since we calmly accept its dominion over ourselves and our societies. The current financial crisis can make us overlook the fact that it originated in a profound human crisis: the denial of the primacy of the human person! We have created new idols. The worship of the ancient golden calf (cf. Ex 32:1-35) has returned in a new and ruthless guise in the idolatry of money and the dictatorship of an impersonal economy lacking a truly human purpose. The worldwide crisis affecting finance and the economy lays bare their imbalances and, above all, their lack of real concern for human beings; man is reduced to one of his needs alone: consumption.
56. While the earnings of a minority are growing exponentially, so too is the gap separating the majority from the prosperity enjoyed by those happy few. This imbalance is the result of ideologies which defend the absolute autonomy of the marketplace and financial speculation. Consequently, they reject the right of states, charged with vigilance for the common good, to exercise any form of control. A new tyranny is thus born, invisible and often virtual, which unilaterally and relentlessly imposes its own laws and rules. Debt and the accumulation of interest also make it difficult for countries to realize the potential of their own economies and keep citizens from enjoying their real purchasing power. To all this we can add widespread corruption and self-serving tax evasion, which have taken on worldwide dimensions. The thirst for power and possessions knows no limits. In this system, which tends to devour everything which stands in the way of increased profits, whatever is fragile, like the environment, is defenseless before the interests of a deified market, which become the only rule.
No to a financial system which rules rather than serves
57. Behind this attitude lurks a rejection of ethics and a rejection of God. Ethics has come to be viewed with a certain scornful derision. It is seen as counterproductive, too human, because it makes money and power relative. It is felt to be a threat, since it condemns the manipulation and debasement of the person. In effect, ethics leads to a God who calls for a committed response which is outside of the categories of the marketplace. When these latter are absolutized, God can only be seen as uncontrollable, unmanageable, even dangerous, since he calls human beings to their full realization and to freedom from all forms of enslavement. Ethics – a non-ideological ethics – would make it possible to bring about balance and a more humane social order. With this in mind, I encourage financial experts and political leaders to ponder the words of one of the sages of antiquity: “Not to share one’s wealth with the poor is to steal from them and to take away their livelihood. It is not our own goods which we hold, but theirs”.[55]
58. A financial reform open to such ethical considerations would require a vigorous change of approach on the part of political leaders. I urge them to face this challenge with determination and an eye to the future, while not ignoring, of course, the specifics of each case. Money must serve, not rule! The Pope loves everyone, rich and poor alike, but he is obliged in the name of Christ to remind all that the rich must help, respect and promote the poor. I exhort you to generous solidarity and a return of economics and finance to an ethical approach which favours human beings. 
No to the inequality which spawns violence
 59. Today in many places we hear a call for greater security. But until exclusion and inequality in society and between peoples is reversed, it will be impossible to eliminate violence. The poor and the poorer peoples are accused of violence, yet without equal opportunities the different forms of aggression and conflict will find a fertile terrain for growth and eventually explode. When a society – whether local, national or global – is willing to leave a part of itself on the fringes, no political programmes or resources spent on law enforcement or surveillance systems can indefinitely guarantee tranquility. This is not the case simply because inequality provokes a violent reaction from those excluded from the system, but because the socioeconomic system is unjust at its root. Just as goodness tends to spread, the toleration of evil, which is injustice, tends to expand its baneful influence and quietly to undermine any political and social system, no matter how solid it may appear. If every action has its consequences, an evil embedded in the structures of a society has a constant potential for disintegration and death. It is evil crystallized in unjust social structures, which cannot be the basis of hope for a better future. We are far from the so-called “end of history”, since the conditions for a sustainable and peaceful development have not yet been adequately articulated and realized.
 60. Today’s economic mechanisms promote inordinate consumption, yet it is evident that unbridled consumerism combined with inequality proves doubly damaging to the social fabric. Inequality eventually engenders a violence which recourse to arms cannot and never will be able to resolve. This serves only to offer false hopes to those clamouring for heightened security, even though nowadays we know that weapons and violence, rather than providing solutions, create new and more serious conflicts. Some simply content themselves with blaming the poor and the poorer countries themselves for their troubles; indulging in unwarranted generalizations, they claim that the solution is an “education” that would tranquilize them, making them tame and harmless. All this becomes even more exasperating for the marginalized in the light of the widespread and deeply rooted corruption found in many countries – in their governments, businesses and institutions – whatever the political ideology of their leaders.