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.
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.)