There are two dominant ways of looking at what is and is not scientific. Neither of them ever considers any theory 'verifiable'. The kind of truth that has constructive verification is not something science really has access to, perhaps outside of mathematics, and there only by convention.
One of them is Kuhn's notion. It focuses on science as a communal activity. The basic idea is that sciences work within paradigms, and that when a paradigm cannot be convincing to a critical mass of invested practitioners, it is abandoned. Then our understanding moves forward sociologically, not based on its content, but on the intellectual honesty of its practitioners. Those who cannot make their case, but insist on operating on a discredited paradigm are being intellectually dishonest, and have become invested in their own paradigm over the progress of the explanatory mechanism as a whole.
The other position is Popper's, focused on individual theories. It considers a theory scientific if it is applicable, falsifiable and parsimonious. Theories that are not 'applicable', i.e. that predict falsely at their inception, are not good candidates for truth. But a theory must go beyond that, and honestly risk 'falsification'. It must predict solutions to problems that are currently debatable. Otherwise it becomes a simple repository of memory, a craft and not a science. If those predictions do not pan out, other contending theories should be used to complement or replace the theory in question. At the same time, to prevent the result from becoming an intractable pastiche of theories that really have nothing in common, each theory should be judged according to its 'parsimony', the degree to which it does or does not truly require additional vocabulary and different ways of thinking. Theories that can let other accepted theories do most of their heavy lifting are preferable, in that they are more likely to merge into a single overarching theory and make science itself simpler to use. But if those underlying theories fail, then the whole content of the reliant theory subsumes the complexity of the working part of the failed underlying theory. (So, for instance, when chemistry was created, 'humour theory' consequently became much less parsimonious, and highly questionable. Other alternatives that were no more effective, but only equally effective with less complexity, largely won over the practice of medicine.)
Homeopathy is discredited sociologically, in that its working assumptions are based upon alchemy, which has been replaced by chemistry as a predictive basis. And it is not parsimonious, in that it is complicated, but one cannot make the case experimentally the complexity actually improves its performance.
Don't take this as an attack on old-fashioned medicine as a craft. There is a lot of room for effective unscientific medicine.
For instance, several forms of psychotherapy are equivalent to the 'client centered' approach in effectiveness. 'Client centered' therapists simply cultivate a way of being honestly interested in their clients in a way that does not require a mechanism or theory. But most people cannot do it very well, outright. Therefore we fall back on mechanisms and habits that produce that attitude within us, or the equivalent complementary attitude within the client -- theories of behavior, investment in family dynamics, etc. Those theories are seldom parsimonious, and they are generally unfalsifiable, or even outright unapplicable. So, in the end, the process is primarily still wholly unscientific.
At the same time, a vast majority of the curative power of physical medicine is also psychological, in a way we still have very little access to or control over. If you can offer a more convincing placebo with extra machinery, more side-effects, or magical explanations for the reasons behind your suggestions, you may still be doing effective medicine, if quite bad science.