I'm more or less in Tom's camp here. Part of the confusion, to me, is that I think he's arguing against a bit of a strawman:
The conflict between the Naturwissenschaften and the Geisteswissenschaften goes back at least two centuries, and became intensified as ambitious, sometimes impatient researchers proposed to introduce natural scientific concepts and methods into the study of human psychology and human social behavior. Their efforts, and the attitudes of unconcealed disdain that often inspired them, prompted a reaction, from Vico to Dilthey and into our own time: the insistence that some questions are beyond the scope of natural scientific inquiry, too large, too complex, too imprecise, and too important to be addressed by blundering over-simplifications. From the nineteenth-century ventures in mechanistic psychology to contemporary attempts to introduce evolutionary concepts into the social sciences, “scientism” has been criticized for its “mutilation” (Verstümmelung, in Dilthey’s memorable term) of the phenomena to be explained.
This doesn't strike me as a critique of science, it strikes me as a critique of bad
science. Scientists do love to model things mathematically, but the flipside of that is that they often have a better sense for when the model sucks. Economics is an obvious example, and generally I get the impression that tons of physicists have been happy to point out the shortcomings of Walrasian economics over the years.
As another example from the first page that jumps out at me:
The emphasis on generality inspires scientific imperialism, conjuring a vision of a completely unified future science, encapsulated in a “theory of everything.” Organisms are aggregates of cells, cells are dynamic molecular systems, the molecules are composed of atoms, which in their turn decompose into fermions and bosons (or maybe into quarks or even strings). From these facts it is tempting to infer that all phenomena—including human actions and interaction—can “in principle” be understood ultimately in the language of physics, although for the moment we might settle for biology or neuroscience. This is a great temptation. We should resist it. Even if a process is constituted by the movements of a large number of constituent parts, this does not mean that it can be adequately explained by tracing those motions.
But this is a cartoonish view of the goals of science. No mature scientist is going to argue with the last part. There is a substantial body of physics (statistical mechanics) developed to elaborate exactly this line of argument but showing that you can still get quantitative information out anyway.
He makes some good, non-controversial points but then seems to ignore them when inconvenient for his argument. To wit: he mentions that science is not a monolithic entity ("The enterprises that we lump together are remarkably various in their methods, and also in the extent of their successes") but then says a couple paragraphs later that historical linguistics and paleontology have similar evidential standards, ergo natural science and social science are totally on the same footing. Hrm.
Anyway, I started skimming at the end because I wasn't finding much of particular interest.
EDIT: If we define scientism in the way Aaron suggests, then I'd say I subscribe to some form of it. While I'm not convinced that Popper's ideas are the be-all and end-all of science, I do think that falsification is an important idea. And that's where I think science beats the humanities in terms of knowledge - it's a lot easier to demonstrate that scientific ideas are wrong than it is in the humanities or social sciences. This isn't to say there's no value in those other things, but whatever value there is should probably be not thought of in terms of knowledge.