Psychiatrists - and doctors generally - see two kinds of symptoms. There are the 'classic' symptoms that have meaning because they signify something we can treat, and the 'off-road' symptoms that don't seem related to any disease process we understand.
In psychiatry, the former are typified by people who are having frank hallucinations and delusions. I know how to recognize them - they look ill, odd, off - and how to treat them - antipsychotics, patience, consideration.
Then there are people who report experiences that are just... not what one normally talks about. I do brief screenings for psychotic symptoms on all of the patients I see, many of whom may have, e.g., mood or anxiety issues, but certainly no evidence of a psychotic disorder. They may be sad or nervous or emotionally disordered, but their reality testing is absolutely intact. When asked if they've ever "seen things others don't see," or heard things others don't hear, they typically hesitate. Then they preface with, "Well, I don't think it's relevant..." or "I'm not crazy, but..." and I know what I'm about to hear.
There was the twenty-two year old girl who said "My sister and I see ghosts. It's accepted in my family, it's not a problem." There was the sixty-four-year old Vietnam Vet who heard music when he saw mountains. It was real music, heard aloud, and specific for each peak.
Musical hallucinations seem to be an entirely different kettle of fish from the angry, insulting voices that are typically heard by psychotic patients. (Oliver Sacks has written eloquently about music and the brain.)
In my short time as a psychiatrist I've already heard many variations on these themes. They seem a class apart from the psychotic symptoms that are familiar to doctors and treatable.
In fact, this sort of phenomenon is seen throughout medicine. For doctors, there are two types of complaint: those that signify a known pathological process, and those that don't have a cause we understand. Most doctors put the second type of complaint in the "all-in-your-head" category. They may be more or less sympathetic to patients with these complaints (often less, and sympathy tends to correlate inversely with the doctor's workload), but they don't know the cause of the symptoms and there doesn't seem to be an underlying disease they can treat, so they're not really interested.
This gives rise to the common complaint among patients that "the doctor doesn't listen to me." It's not that he isn't listening, it's that he's categorizing your problems as "meaningful" and "meaningless." If you tell your doctor your skin is turning yellow, he'll be all ears and will likely order a battery of tests. If you tell him you have a pain in your left elbow that only happens after you eat, he'll say "uh-huh" and try to move on quickly. That kind of pain isn't a symptom of any disease he knows of, so he'll file it under "random aches and pains" and turn his attention to more pressing matters.
Of course, patients rarely know the difference between the significant symptoms and the insignificant ones (that's what medical school is for), so they can get understandably upset at getting yes-deared by the doc.
In psychiatry, these sorts of off-road symptoms fall even further by the wayside than do the general medical aches and pains, because they tend not to bother people. Few people come to psychiatrists complaining of seeing ghosts or hearing music; rather, they accept these things as part of their lives, and the experiences only come to light if they happen to come to a psychiatrist for another reason.
Symptoms can sometimes move from the all-in-your-head category to the now-I'm-listening category when we come up with an explanation or a treatment for them. A lot of people with the fatigue and joint pains characteristic of chronic Lyme disease got the brush-off from doctors before the cause of the disease (a spirochaete transmitted by tick bites) and the appropriate treatment (antibiotics) were identified.
I doubt we will ever find a 'cure' for the off-road symptoms seen in psychiatry, for the simple reason that most people who have them don't particularly want to be cured. I would, however, be extremely curious to see whether we might find an explanation. Are these really psychiatric phenomena, or are they something else?