The argument he's trying to refute (Andrew Glyn seems to be his most immediate target) is that the strength of the working class under conditions of sustained full employment became a barrier to profitability and further accumulation. Brenner says no, no, it wasn't the working class, it was inter-capitalist competition, leading to overinvestment in manufacturing which put pressure on profits.
I'm not convinced: First of all, he limits his evidence against Glyn et al. to movements in real wages and productivity, which seem more in the nature of debater's points rather than real arguments, given that people who seriously make the opposing case talk about a much broader range of ways in which a strong working class can impede capital accumulation: pressure on wages and productivity, yes, but also inflation (didn't people use to talk about "monetized class struggle"), increased government spending, political unrest, and capitalists' fears of all of the above. Second, he never addresses the logic of the case--he never tries to explain why, contra Kalecki (and lots of other people, including the one whose successor he's supposed to be), sustained full employment is OK by capital. He never even tries to make a positive case that employers can dispense with "the power of the sack" with equanimity.
As to his own theory--a couple of people have pointed out that his argument resembles Michael Perelman's, but as I recall from The End of Economics, there's a distinction between the pathology of competitive markets, which is Perelman's focus, and excess capacity, which is Brenner's. Actually there's a well-established argument that a certain degree of monopoly is essential for profitability, investment, and innovation--a line of reasoning that might lead to the conclusion that the way to renewed profitability is increased concentration on a global scale, through mechanisms like the Daimler-Chrysler merger, the fire-sale of East Asian industrial capacity to Western firms, etc. Oddly, Brenner doesn't engage this line of argument at all, maybe because he's working at a level of aggregation where industries let alone firms basically don't appear.
More importantly, his argument seems to be fatally undermined by its surreptitious dependence on the position he claims to refute. As far as I can tell, excess capacity is synonymous with insufficient demand, so why couldn't a crisis of the sort Brenner describes be solved through Keynesian demand-enhancing strategies? Brenner's answer, that this would only keep inefficient producers in business and thereby prolong the crisis, seems incoherent: if there were sufficient demand for the products of the world's industries, there'd be no need to eliminate the inefficient producers in the first place. Isn't it much more convincing--and more respectful of the real historical context--to suggest that governments didn't pursue demand-enhancing policies because of the fear that those policies would further strengthen the working class? Brenner himself gives support to this view when he points out that full-bore Keynesianism was attempted only in the US in the 80s, that is, only where, and once, the power of labor had been decisively broken. But of course if you accept that there has been a crisis of overproduction only because governments haven't adopted demand-enhancing policies, and that this in turn is because of the power those policies would give the working class, then Brenner's story turns out to be the old wage-squeeze account in disguise. So why all the heavy breathing about "competition"?
I think a lot of the essay's weaknesses stem from Brenner's rather shocking disinterest in any theorist besides himself--did anyone else notice that he manages his entire discussion of the Asian crisis with not a single citation from anywhere except the Financial Times, The Economist, Business Week and the New York Times? (I guess no one on the left, or in Asia, has had anything to say about it.) But clearly the root of the problem is his determination to excise class struggle from history. What I can't understand is, why have so many people who I know don't want any part of that project been cutting him so much slack?
Any thoughts on any of the above? I know there was a discussion here when the thing first came out--Rakesh had some very interesting comments--but I'd be anxious to hear from more people, now that there's maybe been more time for digestion.