There are problem with methods. Methods according to Feyerabend means Meta-hodos — The Way After . . .
In other words Method is a way for others to follow after the one who discovers a something. How the discovery happens cannot be contained in any method, especially if the discovery in some way an Emergent Event — For instance the Einstein’s or Newton’s or Galileo’s Revolutions. Or the emergence of a phenomena like super-conductivity, or black holes, or microwave background radiation, or dark energy, or dark matter, or quantum mechanics, etc. Discovery cannot be done by method. But others can be led to the understanding of the discovery, so that they can replicate the discovery by a method. Science is at the root creative human activity. If we use methods in Science this is really pseudo-science. And that is why there is a lot of wasted activity and money in science, because you can wander around labs your whole life and not discover anything. Look at Russian Science for instance. Take the case of Polywater (http://en.wikipedia.org/wiki/Polywater). It was thought that it might be a new phase of water in capillaries. It became of interest for a while when Western scientists tried to replicate the results of a Russian scientist. But what happened was that the particular Russian scientist had his papers co-authored by the head of the lab when the west became interest in the result, and then he was fired when it turned out that the results were caused by contamination in the water. But the book makes the point that Russian Pharmaceutical Labs never discovered anything, they only reverse engineered what was discovered in the West. Just like they reverse engineered the A bomb or the Concord from stolen designs. Following Methods do not lead to any breakthrough discoveries. What leads to breakthrough discoveries is human creativity, which then is re-engineered a story about how methods were used to get the result, while the methods are really invented after the fact to allow others to replicate the result, and to extend it.
Thus Scientific Method works as a means of replication of the discover’s work. This is crucial, but it has nothing to do with discovery. The idea that methods are used for discovery is a ruse, of Scientists that make it appear as if they are objective (whatever that is). So oddly enough the proof that method works is whether replication is possible, and replication is possible and in fact happens all the time. Replication is essential to the advance of science, but there would be nothing to replicate if human creativity and innovation had not first discovered what is worth replicating.