The popularity of this paper is not surprising. There is a lot of talk in the news now about living wages, income inequality, etc. and inter-generational mobility is economic jargon for how well are children doing relative to their parents. Inequality is less of an issue (assuming it is at all, and I don't think it is) if people are able to rise up through the income ranks regardless of where they start.
The paper has a lot in it and I have not gotten through it all yet but I wanted to share one part now. I hope to have more to say on it in the near future, but for the time being here is a copy of Table 3 from the paper: