Brave New World was first published in 1932 as a satirical vision of a future in which, under a "benign" dictatorship, science and technology would solve man's existential anxiety.
In 1958, Huxley readdressed the same issues in Brave New World Revisited. Among the most important ones are overpopulation, morality, propaganda, brainwashing, chemical advances, and subconscious persuasion. We could add cloning, consumption, and the replacement of traditional religions.
The rulers of Brave New World managed to control overpopulation by abolishing natural conception and providing the right number of cloned creatures for the various roles that would keep life going smoothly and comfortably. In modern society, the only country that exercises population control is China, where family planning policies allowed only one child per married couple between 1979 and 20011, and two children per couple under the revised law. In the rest of the world, particularly in emerging countries, overpopulation results in structural poverty and prevents social mobility.
Modern dictatorships claim that the few who perpetuate in power know better than the rest of the population. Thus, like in the novel, the inhabitants of countries under such governments are deprived of their basic freedoms. Propaganda keeps protest down to a minimum, since the base of the social pyramid is semi-literate, and the semi-literate can easily be brainwashed. Dissenters are imprisoned or systematically persecuted. In this sense, perhaps banishment on an island (Brave New World) was more humane.
You may remember that the characters in Brave New World were provided with soma, a drug that relieved their tensions. The very fact that they experienced feelings of anxiety and inadequacy reveals that the "perfect" system was indeed flawed. In modern society, the consumption of sedatives and/or tranquilizers has been rising dramatically. In many cases, even children are on prescription drugs of this sort.
From the small sample of issues described above, it is clear that modern society has seemingly not solved any of the problems against which the novel tried to warn mankind. Rather, unawareness of these issues is driving modern society to the edge of an economic, spiritual, and moral precipice.