Diversity patterns clearly evidence adaptive selection in pigmentation genes in Africans and Asians. In Europeans, the evidence is more complex, and both directional and balancing selection may be involved in light skin. As a result, different non-African populations may have acquired light skin by alternative ways, and so light skin, and perhaps dark skin too, may be the result of convergent evolution.
As noted above the paper, which is provisional and subject to later reedits, does some analysis of gene expression and doesn't find clear differences between fair and dark individuals that one would expect. Then it goes off on a tangent interpreting various statistical tests of natural selection, especially Tajima's D, on a few loci in various populations to offer up a very complex picture of varieties of selection and neutrality on the genes which result in variation on skin color. I think complex, or at least more subtle than we understand, is right, but I'm not sure that this paper hits the right nails on the head. Specifically, I'm a little skeptical a priori for claims of overdominance and diversifying selection. If it was the latter it seems likely that selection was operating on something besides skin color, such as hair or eye color as Peter Frost has argued. As for overdominance, I'm generally convinced by Richard Lewontin's model which suggests that ubiquitous heterozygote advantage is not theoretically possible. Ergo, one must assume that balancing selection has not been a very pervasive dynamic in human evolutionary history. There are some classic examples, especially on malaria adapted loci, but there shouldn't be so many because the variance in fitness in the population is just not realistic. Related: My many skin color posts.