It is untrue that 'nature doesn't weed out the unfit anymore.' This is evidenced by the number of computer programmers and physicists that can't get laid, while a semi-aware Bible thumper can pop kids out by the dozen. You can dislike the criteria used, but natural selection is definitely in play.
I see nothing wrong with eugenics in and of itself. Humans have used it with success since the first plant and animal were domesticated. However, there are certain problems inherent in applying it to humans.
First, we don't really understand genetics all that well, or even what is caused by genes versus environment. This is demonstrated by the poster above who believes that it is moral to sterilize the mentally disabled when many of their conditions are either not heritable, or involve rare regressive genes that are unlikely to be passed on. This was actually practiced in the past, resulting in people who were actually perfectly capable of having 'normal' children being sterilized.
Second, human systems tend to become corrupted by special interest groups and politics. Set up a system to reduce life threatening or debilitating conditions, and soon people are forbidden to reproduce because their child is likely to be unintelligent or unattractive.
Third, we don't know what genes may be most viable in the future, or what might happen if we succeed in eliminating certain conditions. As an example, look at sickle-cell anemia, which is purely disadvantageous except in areas where malaria is present. Imagine a strain of malaria appeared that killed 99.9% of people infected, but scientists had eradicated the sickle-cell gene (meaning no carriers with an adaptive advantage). It could mean the difference between an entire population being wiped out and enough people surviving to continue on. An unlikely scenario, but something like it becomes more and more likely the more we try to build the 'perfect' human by removing 'faulty' genes.
In my opinion, the only time that sterilization might be appropriate in the current social and political climate is if a person has a provably heritable condition that would significantly impact the child's viability or quality of life, cannot understand the consequences of reproducing due to a mental defect, and is likely to behave in a manner that will result in conception. As for everyone else, they have a vested interest in their child's future, so provide them with the tools they need to ensure that children will be born healthy, including things like genetic screening and birth control.