A couple of thoughts...
Economic disparity is not a problem by itself. E.g. if one person is very rich and another is very, very, very rich, this disparity is not an issue. The issue is how many people are truly poor.
If people in this country were economically upward mobile for a long period of time, this might be one reason it is harder now. If I am better off than my parents, it's going to be harder for my children to be better off than me because it is a further step up. A better question would be how many people moved from poor to middle class or from lower middle class to upper middle class and it becomes hard to make an apples to apples comparison.
Great points. In fact this discuss this in the podcast a little bit but not in the paper itself.