This is not so much a problem with the scientific method as a problem with self-interested applications of statistics. F still equals m*a hundreds of years later, and that's not about to change.
Yet I wonder if "the" scientific method has in fact been overapplied way past its sweet spot of mechanics and so on. It's by no means obvious that it works as well in, say, medicine, let alone psychology, let alone sociology, let alone economics. The fact that it's the cult of our age perhaps blinds us from asking the interesting questions about its limits.
Medical science seems, sad to say, incompetent (http://care.diabetesjournals.org/content/17/2/152.abstract rediscovers integration, and statistical illiteracy among doctors has been repeatedly reported) and corrupt (conferences in lavish locations, vendor-sponsored efficacy research).
I'm sure there are good researchers, don't get me wrong, but I'm also not surprised that some really questionable stuff gets reported.
I'm sadly, even less aware of the state of research in sociology, but I'd like to point out that non-scientifically-tested psychological theories tend to be complete nonsense (cf. lots of Freud's work). With respect to economics: the field has many problems, but a book like Freakonomics is a very readable argument in favour of the use of statistics in (micro-)economical science and related fields. (Do note that the scientist-author, Levitt, actually understands statistics. This is, I suspect, important.)
That said, there are issues with the scientific method, like the fact that it tells us to drop falsified hypotheses but does not, in itself, teach us how to find interesting results. That's not germane to your observation, though.
One reason the scientific method does not work on economics is that markets are anti-inductive[1]. If you can establish a regular pattern in their behavior, market participants start exploiting that pattern, and it goes away.
I'm not sure this is such a strong attack on the scientific method. First, there's much more to economics than predicting the stock market - a proper understanding of demand curves is useful even if everyone else has it as well. In fact, I'm not sure that predicting the stock market has more to do with mathematics than with mass psychology.
That said, I do agree that properties of the stock market, once widely known, tend to be arbitraged away. From the article:
> There was a time when the Dow systematically tended to drop on Friday and rise on Monday, and once this was noticed and published, the effect went away.
However, that doesn't mean that the scientific method cannot produce true conclusions - it's just that those don't tend to stay true.
lesswrong has much more impressive criticisms of the scientific method, IMHO. (The main one being that, while the scientific method will hopefully prevent you from endlessly clinging to a wrong hypothesis, it won't tell you how to find good hypotheses.)
Oh yes, there are definitely some problems with over-zealous applications of the scientific method (or rather, over-zealous discarding of other methods of reasoning) - but this article doesn't really cover them. Not everything of value can be measured in a double-blind experiment.
What's "the scientific method" you speak of? There main idea behind scientific reasoning is "Look for evidence to test things, don't be afraid to challenge the big boys"
There's quite a bit more to the scientific method than that-- the notions of controlled observation and reproducible results surely matter, as does the principle of parsimonious explanation.
