I really dislike it when people (especially people of a technical mindset like math/physics/CS majors) summarize the above article in the way, and use it to justify their dislike of the social sciences. It's not about the problems of methods in psychology in general, but about blindly applying methods (of any field) without understanding the motivation, underlying assumptions, or unintended consequences behind them.
Most modern psychological research is surprisingly rigorous and depend on sophisticated statistical methods. The results may not be as strong or conclusive as those of, say, chemistry, but for a discipline that has to study something as mercurial as human behavior, it is certainly a useful and worthwhile.
First of all, I am no expert in psychology, and most of my exposure to it was through readings in AI courses.
For a good example of a milestone in modern psychology, consider the Rescorla-Wagner Model--an attempt to model classical (Pavlovian) conditioning in a quantitative manner--which essentially implies that organisms only learn from unexpected events. It not only predicts the degree to which an organism would react to stimuli, but also compensates for something called the "blocking effect," which occurs when something stimulates more than one association and one of those associations overpowers a weaker association, prevent conditioning of the weak association. It is similar to the Widrow-Hoff Least Mean Squares (LMS) learning algorithm that you might learn in a neural networks class. This model is something that has been tweaked and tested under many different conditions and experiments, and the results have been distilled through thorough statistical analysis.
The R-W Model is one part of a dramatic change in our understanding of learning that has occurred in the last couple decades. For a summary of some of these results, Rescorla has an article published about 20 years ago called "Pavlovian Conditioning: It's Not What You Think It Is," [http://jsackur.free.fr/classiques/Rescorla1988.pdf] which should be pretty accessible.
Most modern psychological research is surprisingly rigorous and depend on sophisticated statistical methods. The results may not be as strong or conclusive as those of, say, chemistry, but for a discipline that has to study something as mercurial as human behavior, it is certainly a useful and worthwhile.