Last week I was reading a book on recent advances in astronomy. It seems that astronomers detected that stars in the outer arms of spiral galaxies are moving "too fast" -- in fact, way too fast -- and should just proceed on their own into space instead of orbiting the galaxy, when their velocity is compared with the amount of matter currently known to be in such galaxies.
Here is a classic case of Popperian falsification. The current theory of gravity is falsified, and "bold conjectures" should be forwarded for its replacement. So is that what scientists did? Not at all! Instead, they saved the current theory with an unfalsifiable, ad hoc assumption: galaxies are full of dark matter, which, by its very definition, escapes detection! (That doesn't mean that one day we might not detect it, but it does mean that failures to detect it will never "refute" the theory -- it can always be maintained by assuming the stuff is just really, really hard to detect.)
And what's more, the above is good science, and following the Popperian formula would be bad science. The current theory of gravity is so well confirmed that it would be silly to abandon it without taking a good, long time trying to save it. Now, if in 30 or 40 years, no one has found the dark matter, then it might be time to consider looking at gravity.