I agree that fifteen minutes minus paperwork is shockingly short. Still, there are doctors who do reasonably well at paying attention.

Most of my information is from the fat acceptance community, where there are a great many stories about doctors who just tell fat patients to lose weight*, regardless of symptoms. The typical stories seem to be either "I had to go to three or four doctors to find one who would listen" or "I must be lucky, I have a great doctor". I can't derive a strong opinion about the proportion of attentive doctors from this, though I wouldn't be surprised to find that it's under half.

*I've also seen a few stories from unusually thin people who were simply told to gain weight, and one from a man who (as far as I could tell) was lean and muscular, but was told to lose weight by a doctor who literally only looked at his BMI.

Sure- but if you have some rare symptom, any decent family doctor should say "go see a specialist" and refer you. You certainly aren't going to contact metamed every time you get sick, and for chronic conditions, a specialist (with journal and up-to-date access) is going to be the managing physician. Anything other than routine sniffles, vaccinations and check-ups and you probably have exceeded your family doctor's expertise.

The big problem for misdiagnosis at the family-med level are the hordes of relatively rare diseases with common symptoms, but this is a very hard problem to solve. Having spent some time dealing with this as a statistical problem, even if you have a rare cluster of common symptoms, its usually the case that you are more likely to have a rare presentation of a common disease than it is that you have a rare disease.