It's taking a bit of time to look through this, but I have not seen it before.
I do have some initial reflections:
The basis of their criticism of Marx is the confusion over the historical precedence of exchange and circulating capital to productive capital versus the logical precedence of productive capital over them. As Capital is not a historicist work, there is no reason to believe that the historical order is the same as the logical order, especially as come into a world of generalized commodity production. As such, capital did not subvert its own rules (p. 4) since merchant and usurious capital existed on the fringes of non-capitalist society, and thus money, commodity, value, etc. as constitutive social forms were at best nascent in them, but not yet wholly socially determinate. Once productive capital subsumes the whole of society, non-productive capital only then truly becomes capital.
The confusion brought about by this is immediately evident because they argue that profits were made by the "different socially necessary labor times for the production of a thing". However, socially necessary labor time and exchange-value only have bearing in generalized commodity production, in already capitalist society. As such, the wealth that came from merchant and usury capital does not take the form of value. Petty commodity production was not a mode of production, there was no exchange-value or use-value for that matter, since there was no value. There was no abstract labor or concrete labor. All of those categories only have bearing in relation to capital, that is, in the situation in which M-C-M' will actually work itself out to be M-C...P...C'-M'.
However, it is necessary to begin with M-C-M' because that is how capital appears. This appearance is not false, so much as incomplete. Marx will spend the first 6 chapters moving through different ideas of commodity, money, value, etc. and each chapter is driven to the next by its own inadequacy in grasping capital. The first 6 chapters are about showing why value and surplus-value in generalized commodity society cannot come from exchange, which necessitates beginning with M-C-M', since C-M-C clearly doesn't lead with any necessity to an infinite cycle.
This is also why even if M-C-M' is only how capital appears, it is nonetheless not therefore simply an illusion.
Then there is the common misconception that "capital is a social relation". I would say that Capital is closer to Hegel's notion of Concept in the Science of Logic
"The understanding determines, and holds the determination ﬁxed. Reason is negative and dialectical, since it dissolves the determinations of the understanding into nothing; it is positive, since it generates the universal, and comprehends the particular therein. Just as the understanding is usually taken as something separate from reason in general, so also dialectical reason is taken as something separate from positive reason. In its truth reason is however spirit, which is higher than both reason bound to the understanding and understanding bound to reason. It is the negative, that which constitutes the quality of both the dialectical reason and the understanding: it negates the simple, thereby posits the determinate difference of the understanding; but it equally dissolves this difference, and so it is dialectical. But spirit does not stay at the nothing of this result but is in it rather equally positive, and thereby restores the ﬁrst simplicity, but as universal, such as it is concrete in itself; a given particular is not subsumed under this universal but, on the contrary, it has already been determined together with the determining of the difference and the dissolution of this determining. This spiritual [obviously for Marx 'spiritual' is not the right word - me] movement, which in its simplicity gives itself its determinateness, and in this determinateness gives itself its self-equality – this movement, which is thus the immanent development of the concept, is the absolute method of the concept, the absolute method of cognition and at the same time the immanent soul of the content."
They further go on to talk as if there were such a thing as "simple commodity production" as something distinct from, as a kind of mode of production independent of, capital. Aside from Engels' complete misunderstanding of the matter, I don't see a point in Marx's text that would allow for this reading.
Reading on through, I think there continue to be significant problems with how they comprehend Marx's actual work. It is a bit like reading Marx's critique of Hegel, in that one really feels like Hegel is the name ascribed to the Young Hegelians, and therefore much of the criticism of Hegel as more aptly a criticism of the Young Hegelian reading of Hegel. In the same manner, this essay is wrangling with post-Marx Marxism, and particularly the versions of it that one might call Orthodox Marxism, the Marxism of the 2nd and Third Internationals.
The reason this matters is simply that a lot of what Marx is actually engaged in cannot be read since they see a work like Capital through the lenses of Engels, Lenin, Kautsky, Luxemburg, Pannekoek, et al, and most of this stuff is nearly worthless for us today. Marx, however, retains a freshness that speaks to the moment.
Allow me to give examples.
The first mistake is evident in the idea that Marx's Capital is a critique of capitalist society, and thus Capital is an empirical, historicist text that must project an ideal in order to be coherent. I would argue that that text is nothing of the sort. Marx's work is, firstly, a critique of political economy. Marx is rather explicit about this, as that is the subtitle. Very few people, however, think about that very seriously and so they assume that Marx is simply presenting a better political economy, not a critique of political economy as such, as an attempt to rationally comprehend capitalism as a rational object. This obscure the irrationality that Marx identifies both within capital and political economy.
Instead, we should see Capital differently. It remains immanent to political economy's categories and is a critique of those categories and their insufficiency, and insofar as political economy is capital thinking about itself in a rigorous way, about its being-for-itself if one wanted to borrow a Hegel-ism, Marx considers it scientific, which in his Hegelian sense would mean both ontological and systematic, wissenschraft, not scientific in the natural-sciences sense which takes the object of its investigation for granted. Actually, beginning with J.S. Mill in particular, Marx excoriates as vulgar economics or vulgar political economy the shift from wissenschaft to natural scientific approaches to a decidedly non-natural object.
Capital thus moves like a Hegelian phenomenology of categories taken from within political economy, not proposed from outside of it, developing a "science of logic" of capital through the limitedness of those categories from their abstractness to greater and greater degrees of concretion. As such, the complaint that Marx does not take into account states and cannot explain wars misses that Marx never actually arrives at The State or International Money/Finance because those were supposed to be a part of the 4th volume of Capital, and could only be dealt with at a degree of concretion that was beyond what Marx was able to complete in his lifetime and which was largely never taken up afterwards, with only a few exceptions, prior to the last quarter of the 20th century and even then, as a completely heterodox strand of Marxian thought. One of the more engaging recent pieces on exactly this is Werner Bonefeld's excellent book
A second mistake is to think that Marx is not concerned with realization of value or that he held to a disproportionality theory of crisis. He is explicitly concerned with the realization of value and issues arising from it and all crisis in Marx is logically a crisis of valorization. However, the problems that arise from the failure of realization, from what we might call a part of a crisis of accumulation, could only be partially developed in his incomplete work. It is already implicit, however, in his discussion of value and price and the implication that value and price are never the same in actuality. That is, insofar as the validation of the expenditure of labor, raw materials and means of production into potential values only is realized in exchange, there is always the situation that no individual capital can ever gauge socially-necessary labor time accurately. This is part of the reason that command capitalist economies, rather than market capitalist economies, are so much more rigid and stagnant. Competition between capitals through freely floating prices really is the only way that winners and losers can be sorted out in a way that is not directly distorting (it is indirectly distorting, but that comes back to the problem of the necessity of the critique of value to grasp the social form and nature of crisis, and why competition models fail.)
The third mistake is the attribution to Marx that the overthrow of capitalism is the overthrow of relations of distribution (private ownership of the means of production.) They are quite clearly wrong that "Exproprition of capitalists or the dissolution of the private power of the individual capitalists would thus obviously be the negation of capital", not simply as a statement, but as attributing this view to Marx. Marx's critique is not a critique of distribution, but of the very mode of production itself, and thus of labor, of value, of money, etc. Postone's work has been critical to recovering this dimension of Marx's work (see the recent “The Current Crisis and the Anachronism of Value”)
Of course, they are quite right to reject the idea that overcoming private ownership of the means of production is the end of capital, even if they got there by throwing out the baby with the bathwater. However, they would get much more out of Marx if they gave up reading him through their Leninist-tinted lenses, a tint that they have not because they are Leninists, but because they end up reading Marx through lenses they purport to want to stop wearing. It would make the work of a more adequate critical theory against capital less difficult.
I also fully concur in their statement that Monopoly Capitalist analyses take us away from the critique of capital, that they "blatantly subvert the analyses of value relations i.e. they render impossible the comprehension of the social distribution of labour in commodity economy." This is fully evident not only in obvious ways with writers like Robert Brenner fetishize intra-capitalist competition as the locus of capitalist crisis, and therefore the competition between states as central to crisis, but very much also in what would seem to be quite otherwise critical Marxists, such as Endnotes, which in their last issue largely adopted the stupidity of Brenner, and the British SWP trotskyists who always understood their state capitalism as provable through the competition between states.
The further conclusion that theories of imperialism, oppressed and oppressor nations, etc. is reactionary rubbish is on very solid ground. My complaint would simply be that I sense a tendency (and let me be clear, it is a sense of a tendency, not a claim that this is quite made explicit) in the text to want to shrug aside gender, nationality, sexuality, race, etc as kind of fake and class struggle as real. As I see it, this would be radically false, insofar as it confuses the critique of political economy with a reification of class. Race, gender, sexuality, etc are very much categories of capitalist society and are as connected to the logic of capital as class. I would argue that part of the crisis of communist ideas today is the end of the working class as a third estate, as a social group with its own culture, ideas, and separation from society a a whole. It is also the foundation of the possibility of returning to Marx's work as the critique of labor rather than as the critique of capitalism from the point of view of labor.
I haven't gone though all of their notes, and I probably won't because it is a rehearsal of a lot of things I have read over the years.
That said, I appreciate their attempt to grapple with the present and to abandon orthodox Marxism and I am very sympathetic to their political conclusions, but they need to go rather further with their critique and oddly enough they will not get there without recovering Marx.