My principal criticism of Marx is that, simply put, his model of how capitalism works was restricted to what he saw during the late stages of the industrial revolution in Germany - remember, the Manifesto dates from 1848. It is a model that is properly described as "descriptive," that is, a model that identifies and labels the various components and dynamics of the system it attempts to describe. One of those limitations, as mentioned, is its chronistic nature - Marx and his theories were very much children of their time. Another is Marx's profound misunderstanding of economics. A third is his rather unprofessional grasp of historiography. Let us discuss these.
As for Marx's temporal limitations, I think that much of his criticism of capitalism rests on the essentially exploitive basis of mid-19th-century Continental industrial structure. It incorporated a peasantry that had moved to the city seeking work in industry and was essentially otherwise uneducated and unable to pursue other means of support. This is his "proletariat," and this particular description of it was not the universal one that is so central to his theory, it was, in fact, a very skewed and limited view of the class that was to utilize industry to better itself into the class that he defined as parasitical, the "bourgeoisie," which he mistakenly assumed would wither away. In fact, it ended up subsuming the proletariat, and it used education and the formation of liquid assets that ended up indistinguishable from capital, to do so. Proof of this is seen in the fact that the "proletariat," now very definitely bourgeoisie, are the number one shareholders in U.S. industry through pension and mutual funds. Marx did not anticipate this - it would have run contrary to the basic exploitation which was so central to his model.
Second, Marx's understanding of economics was based on a flawed and thoroughly discredited base, his "labor theory of value," in which risk of investment was essentially discarded as a factor of return. This is the reason that Marxist economies are so profoundly kleptocratic in nature - this theory works fine as long as capital investment is already made and there's something already existing to redistribute. In its absence there is little incentive to invest and little surplus to invest even if there were an incentive. It gets worse, of course, in that Marxist economies are necessarily centrally-planned, a description of economics that is 180 degrees out from every model that had gone before. It was essentially theoretical, not descriptive, and here Marx begins to depart from the descriptive model into an entirely unjustivied "normative" one.
Thirdly, Marx's grasp of historiography and its product, history, is severly limited by his insistence on its basis in class struggle. This isn't in itself a bad model of social dynamics, it is simply a severely limited descriptive model, quite incapable of being expanded into a normative model without encountering consequences that it absolutely did when it met the real world in the form of the Communist Bloc. The problem is threefold - first, that Marx depended on economics to describe class. Neomarxists have expanded this to the holy trinity of race, gender, and sexual preference these days, none of which have anything to do directly with Marx's original model, and for good reason - the latter is not a description of class structure that is valid outside his own time. (Nor, IMHO, is its successor). Second, Marx assumed that class was more important that individual characteristics in describing an individual's relation to society at large. Hence, it is more significant that a person is black, for instance, and hence disempowered ("alienated" was Marx's catchall) than it is that that person may be personally wealthy, and occupying a position of power. This, incidentally, is the basis for the claim that such a person, despite his being a judge wearing a thousand-dollar suit, can never be "racist" because he is "disempowered" - that description comes from his class and not his person. This is a huge weakness in Marxist social theory. Thirdly, Marx modeled class structure after the fairly rigid and unchanging German model of his time, when in fact the American version (even more so than its founder, the Englisn), incorporating a high level of class mobility and opportunity, was the model Western economics and society was to follow, even in Marx's native land.
There is more, much more, and I won't attempt to address it tonight. The upshot is that our present world isn't accidental, it is the result of the failure of a descriptive model to become normative, the failure of a theory to function in the real world because it is insufficiently complex to answer the complexities of the real world. Marx is wonderful to study, provocative, exciting, and very revealing. He is hell to live by.
Anyway, that's what I think.
I would add these observations of my own:
I have always considered Marx's most serious and debilitating flaws to be concerning human nature:
1) he tacitly asserts that man is basically good (in contravention of Judaeo-Christian axioms about man's fallen-ness), and
2) he posits that man truly thrives on work and loves to be about it.
Now, since all of his deliberations and prognostications were predicated upon his model of human nature, it is not surprising to me that he got it so wrong. Fundamentally, man is covetous, prideful and rebellious. And it is NOT because he is corrupted by institutions; it is because he is born needing redemption. Civil constraints have happened, historically, because of these tendencies. Only the redemptive qualities engendered by the knowledge of the holy have successfully mitigated against them -- and it is these very qualities that Marx vehemently denied, thereby decapitating his hope of ever being correct. Wrongly assess man, wrongly assess man's future.
And as for man "loving work", that is the very calumny which most singularly brought Russia down (they had their famous "zero unemployment", and everybody got paid [not much, though; in fact, I heard a cute little joke when I was over there in 1987: "We pretend to work, and they pretend to pay us"]; it's just that nobody bothered to show up, and if they did, they goldbricked the days away) -- because, given the opportunities (and how we do search for them), man will sometimes work harder to get OUT of doing work than he would have had he actually done the work itself.
Those are the facts. Any thinker who fails to deal with them has his head in the clouds, or some place where the sun doesn't shine.
Oh, it's even worse than that - Marx himself explicitly rejected such things. The only true consciousness for Marx was class-consciousness. Race, gender, sexuality - these were all false consciousnesses as far as Marx was concerned. It's not a stretch at all to imagine that Marx would personally reject much of what passes for "Marxism" these days.
And therein lies the trouble for latter-day Marxists. Marxism-as-Marx-described-it is fundamentally broken, so to resurrect it, one has to heavily revise and extend his work. But in so doing, you very quickly find yourself completely at odds with the guy who's supposed to be your patron saint...