Karl Popper was a 20th century philosopher of science, best known for his work on falsifiability. He was critical of the ideas put forth by previous philosophers such as Carnap, that science works by verifying your theories through examination of the world. He said that many theories that were not scientific could be successfully verified by either making vague predictions, or through ad hoc adjustments to the theory. For example a horoscope can predict something vague like “you will have a pleasant surprise later this week”. Then you find some forgotten money in your pocket, and the horoscope was seemingly verified to be true! However since nearly anything could have verified it, since it was so vague, this does not count as science.
He was particularly critical of Freud’s theory of psychoanalysis and Marx’s theory of historical materialism, both of which were considered scientific by many at the time, but seemed to explain almost all sets of observable data. Instead he suggested that scientific theories must put forwards highly specific predictions, and the scientists must then work to falsify, rather than verify, the theory.
Popper’s (non-Marxist) disciple Paul Feyerabend pretty well undermined Popper’s view, essentially showing that many interesting and foundational scientific discoveries could not have been made if we exclusively followed the mode of what Popper calls science.
Absolutely, because it depends on how you define “vague”. For example, for a long time proving that Earth revolves around the Sun was considered good science, regardless of the fact that it does not constitute what is the orbit like. Then it became refined into “circular”, then “elliptical” and so on. So the vagueness changes with time to becoming less and less vague.