1. We must ask, why does one get punished for something he or she cannot remember having done in a previous life?
If you knew what had happened in your previous lives while in a new incarnation, than it would render your free will moot. Therefore, as a soul, you agree to come into the world under certain conditions. You are destined to meet certain people, because you prearranged it. But, because you have free will in this life, you may or may not follow thru on those desires when you get here.
The idea that we have to come back to correct something is a very christian ideal. It is based on dichotomous thought ~ the idea that everything is either good or bad. Often, we agree to come here for the simple life experience. Whether you view that experience as good or bad, it is your experience.
2. If the purpose of karma is to rid humanity of its selfish desires, then why hasn't there been a noticeable improvement in human nature after all the millennial of reincarnations?
Have you noticed that there are a lot more of us now than before? That is a lot of souls seeking out their own way. As we progress thru our incarnations, we tend to move from the banal and physical, to the intrinsic and instinctual. That which is pleasureable for it's own sake, not out of some value applied by the social dogma of the time.
3. If reincarnation and the law of karma are so beneficial on a practical level, then how do advocates of this doctrine explain the immense and ever-worsening social and economic problems, including widespread poverty, starvation, disease, and horrible suffering in India, where reincarnation has been systematically taught through out its history?
On a practical physical level, or on a practical spiritual level? Most of the beneficial things we learn about life come thru pain and suffering, not thru instant gratification, or the accumulation of material goods. Those that are materially comfortable tend to overlook the basic beauty and value of life. Perhaps those we view as suffering are better off than all of the people in the civilized world. They often tend to be more content and centered, even in their suffering. Whereas people that are materially wealthy seem to never be happy or satisfied in their lives.
Christianity seems to me, to operate on a value added system, whereas those that believe in karma and reincarnation tend to believe in more of a value neutral system. Christians seem to need to know that they are happier than thou, whereas I simply need to know that I am happy, and no one else has anything to do with it.