During Galileo's time, people still believed in an ancient model of Aristotle's, who said that heavier objects fall faster than light ones. Some of Galileo's contemporaries apparently confirmed this using experiments (how that happened I don't know!), but a young Galileo noticed during a storm that bigger and smaller hailstones fell to the ground at the same time. When he pointed this out, his contemporaries said that Aristotle must still be right and that therefore the bigger hailstones must have started from higher up. This could have been true, but the clue, with hindsight, to this kind of intellectual laziness is the ad hoc way they had to set up the hypothesis. They had to place the hailstones' formation heights at exactly the right level so they would fall together. In other words, this model was not predictive because they had to 'fine tune' it by hand to get things right, and the setup was different in each case, depending on the size of the bigger and smaller hailstones. Galileo had a more elegant model that said all the hailstones fall at the same speed, which was right but unfortunately, did him very little good in his lifetime, and it took the bloody-minded obstinacy of Isaac Newton, who also lived in a freer environment, to mathematically ram this idea into the mainstream.
Four hundred years later, there's a similar problem. The standard theory of gravity: general relativity, was devised before galaxies were even known about. It has performed well on the Solar system scale (Gravity Probe B) and at other high accelerations (binary stars), but physicists are now applying it to galaxies which are ten orders of magnitude bigger than the Solar system and have accelerations at their edges ten orders of magnitude smaller. No theory has ever survived a translation over ten orders of magnitude of scale: when they tried in the 19th Century to apply normal mechanics to tiny atoms (a ten order of magnitude scale difference) it didn't work at all. Max Planck had to invent the bizarre quantum mechanics. Sure enough, on applying general relativity to huge galaxies, massive problems have appeared. The mainstream theorists have responded, without showing the imagination of Max Planck, by adding huge amounts of an invisible kind of new matter (dark matter) to the galaxies in just such a way (in an halo around them) that for each case general relativity agrees with the observed rotation, but as for the case of the hailstones in the 15th Century, this hypothesis of dark matter is not predictive. The theorists are 'tuning' the observations of mass to make general relativity fit the observed rotations, and differently in each case. The only reason this hypothesis has survived without any detection of dark matter after 40 years of looking, and billions of pounds of funding, is a kind of group-think that would not be out of place in a religion.
How can this intellectual logjam be broken? History has shown that it is not enough to invent an more elegant alternative (as I have done with MiHsC). The only way to counter such an intellectual blockage is to find an anomaly for which the old theory has to be modified in such a Byzantine and embarrassing manner that it looses its credibility. In this case, the problem of globular clusters could do the trick, eg, see this blog entry.