Phenomenalism as a theory of truth is a form of reliabilism.
What can be justified - or verified - has meaning,
what cannot be - at least potentially - is nonsense.
The methods used to verify statements are traditional empirical and scientific ones - ie the senses plus scientific equipment. As such, it is open to some of the same criticisms as reliabilism itself.
However, perhaps the main problem with the approach is that the verification principle itself is too vague. How is a statement verified?
Maths and logic are also problematic for this theory in that they are truths that seem to be independent of sensory verification.
Ayer's answer to this was to consider them conventions of language. Similarly, all ethical and aesthetic statements were held to be neither true nor false because they could not be verified.