The philosophy in which falsifiability, or its close relative verifiablilty, is the criterion for meaning is known as logical positivism. It was all the rage in the mid-twentieth century.
The verification principle states that no statement has any meaning unless it is, at least in principle, verifiable.
The problem is that the verification principle is itself a statement and cannot, even in principle, be independently verified. The principle fails its own test and by its own standard is therefore itself meaningless.
Thus, meaning has to be sought elsewhere.
The great proponent of logical positivism was AJ Ayer. You might like to check out his classic text on Language, Truth and Logic.
On the matter raised by Uranus, we may note that even scientists sometimes make mistakes. Newtonian gravity is in principle falsifiable because we can look for cases where it does not apply. This is nicely illustrated by the orbits of Uranus and Mercury. Anomalies in the first proved to be down to Pluto, in the second to Relativistic effects which rendered Newton obsolete.
Some developments in theoretical physics are proving difficult to say whether they are falsifiable or not. String theory is a good example, where almost any fundamental theory of physics can be modelled by modifying the strings to match experimental results. As a consequence, the accusation goes, it is not falsifiable and is therefore metaphysics and not physics. On the other hand string theories to date all assume supersymmetry, and experimental evidence is growing to suggest that reality may not be supersymmetric. So if reality is supersymmetric then string theory may be just metaphysics, but if reality is not supersymmetric then string theory is falisfiable. It is too early to say. Everett's parallel universes provide another example which is probably untestable, while all the many "interpretations" of quantum mechanics have been branded as such because they have all proved so utterly unfalsifiable.
Nevertheless, one cannot deny that these theories have had a profound impact on theoretical physicists - they don't stop to ask whether an idea is falsifiable or not before they start playing with equations, they work out the theory first and worry about the question afterwards.
Falsifiability is therefore not very useful in exploring the frontiers of knowledge, only as a periodic sanity-check on what has been achieved to date.
In science, falsifiability is thus a pragmatic issue; is it conceivable to brew up an experiment to test the statement? This contrasts to falsifiability in philosophy, which is more of a logical issue; is it possible to refute the statement in any way at all?