Brian Leiter, commenting on the modern rejection of the empirical claims of Marxism, writes:

But what empirical evidence, it may fairly be asked, is there in favor of Marx’s theory? To start, of course, there is the enormous and impressive historical literature employing a Marxian framework to make explanatory sense of historical events. Perhaps more striking is the accuracy of many of Marx’s best-known qualitative predictions about the tendencies of capitalist development: capitalism continues to conquer the globe; its effect is the gradual erasure of cultural and regional identities; growing economic inequality is the norm in the advanced capitalist societies; where capitalism triumphs, market norms gradually dominate all spheres of life, public and private; class position continues to be the defining determinant of political outlook; the dominant class dominates the political process which, in turn, does its bidding; and so on. To be sure, there are striking predictive failures in the Marxian corpus like the labor theory of value, the theory of the falling rate of profit, or his mistaken views about timing.

Each claim is equipped with a footnote with the relevant evidence. Let's go through these.

To start, of course, there is the enormous and impressive historical literature employing a Marxian framework to make explanatory sense of historical events.

It is unclear whether this is a testament to the predictive power of Marxism, or to the propensity of academics, and Academic Marxists in particular, to write books applying their pet approaches to history.

The rest of the claims we can divide into two parts: the plainly false claims, the unclear claims, and the commonly agreed on claims.

Let's begin with the plainly false.

...growing economic inequality is the norm in the advanced capitalist societies

The footnote supporting this is

See Frank Levy and Richard Murnane, “U.S. Earnings Levels and Earnings Inequality: A Review of Recent Trends and Proposed Explanations,” Journal of Economic Literature 30 (1992): 1333-1381, and, more generally, Edward Wolff, Top Heavy: The Increasing Inequality of Wealth in America and What Can Be Done About It (New York: Twentieth Century Fund, 1995). And for a more recent, popular treatment, see Paul Krugman, “For Richer: How the Permissive Capitalism of the Boom Destroyed America’s Equality,” New York Times Magazine (October 20, 2002), pp. 62 ff.

I wonder if Leiter has read all the items he cites. Indeed, growing economic inequality has not been the norm in America. From the times of the new deal, America had become more equal; this fact is amply documented in the the "popular treatment" of Paul Krugman (see here) that Leiter cites. Krugman's point is that the recent growth in US inequality since the 80s is not typical of the US capitalist experience.

But even the recent US experience is far from the norm among industrialized societies. This analysis of the experience of five industrialized nations shows that, in fact, Sweden and Germany has remained the same from the 1970's to the mid 1990's in terms of inequality; Canada has actually become more equal; while the US and the UK have become more unequal. In short, its simply untrue that "growing economic inequality is the norm in the advanced capitalist societies," as Leiter claims.

Next, Leiter writes,

...class position continues to be the defining determinant of political outlook

and in support cites,

See, e.g., Eric Mann, “’Foreign Aid’ for Los Angeles: Three Myths of Urban Renewal,” New York Times (May 1, 1993), p. A23 (“Elect a black mayor. In 1973, a multiracial movement elected Tom Bradley, a moderate who promised jobs and justice. The Bradley legacy has been a revitalized downtown business district, the transformation of the mayor’s office into an adjunct to the Chamber of Commerce and the polarization of wealth and poverty. At every major juncture, the Bradley administration sided with privilege and against the poor”); Katha Pollitt, “Subject to Debate,” The Nation (December 4, 1995), p. 697 (“The truth is, except on a few high-profile issues--abortion rights, sexual harassment, violence against women--electoral feminism is a pretty pallid affair: a little more money for breast cancer research here, a boost for women business owners there. The main job of the women is the same as that of the men: playing toward the center, amassing campaign funds, keeping business and big donors happy, and currying favor with the leadership in hopes of receiving plums”). For one scholarly treatment, see Clem Brooks and David Brady, “Income, Economic Voting, and Long-Term Political Change in the U.S., 1952-1996,” Social Forces 77 (1999): 1339-1374.

Any careful reader will note the rather larger disconnect between the claims and the evidence provided for them. A black mayor takes some stances some progressives don't like! Feminists try to curry favor with the leadership! The scholarly treatment cited by Leiter also says nothing of the kind. What it does say is the following:

...cumulative changes in mean household income have had a very large effect on the outcome of presidential elections since the 1950s...we discuss the contributions of this study to understanding income as an important but underappreciated source of political change in the U.S.

At no point does it claim that class position is the "defining" determinant of political outlook. Further, merely because Americans tend to vote for the incumbent President if the economy has improved his administration, it does not follow that it is class that determines the outcome.

Incidentally, looking at the exit polls of the last two elections, we see that church attendance has been as good or better determinant of political affiliation.

Next, the unclear claims, Leiter writes,

the dominant class dominates the political process which, in turn, does its bidding

Whether any of these things are taking place now, more than before, is questionable. The dominant class always has always had influence on the political process, by virtue of their money, influence, and interests (compared to the apathetic voter). Whether this is true now, more so than before, is questionable and none of the books/articles Leiter cites make the case.

the gradual erasure of cultural and regional identities...

Similarly, cultures are always getting erased, due to war, migration, and so on; they also evolve due to the progress of technology, contact with other cultures, and so on. One would expect this process to speed up with the progress of technology and the increased contact between different parts of the globe. In this case, Leiter actually does cite a source that supports what he was written ( a rare occurence indeed), George Ritzer's The Globalization of Nothing. But Ritzer's opinion is not a majority one, and whether capitalism per se has increased the erasure (rather than evolution) of cultural identities is unclear - others argue differently. In short, Leiter's supporting evidence here is as disputed as the original thesis.

As for the rest of what Leiter writes,

capitalism continues to conquer the globe; where capitalism triumphs, market norms gradually dominate all spheres of life, public and private

it is, in some sense, commonly agreed on. You do not need to be a Marxist to believe in these two statements (or, indeed, even in those that I labelled unclear or false). Pretty much every theory that tends to look at capitalism in a positive light will predict that it will spread; and that its spread will cause cultures and nations to evolve. Whether any of it can be cited as a testament to the predictive power of Marxism is doubtful, to say the least.