Doctors and dentists, possible explanations:

I was actually planning to go somewhere specific with the doctors and dentists per capita idea, but I got distracted into wondering what was the reason for the discrepancy. I had a theory going that it could be related to age. After all, older people might receive more medical care, and thus need more doctors, while regular dentist visits seem to be something that happen to kids more often than adults.
So, I took median age data from the US Census (although, as you know bob, median age doesn't totally represent age distribution in a popualtion).

First, for doctors:
There is a pretty strong correlation here, which is even stronger than "the formula" would attest to, (which is why I like looking at the graphic of a scatterplot, rather than just teh equations). Like many scatterplots, there seems to be something of a crescent shape. There are young states without many doctors, old states without many doctors, and old states with lots of doctors...but no young states with many doctors. There could be several reasons for thus, including my original thesis, or it could be that states with high median populations tend to be affluent with smaller family sizes, are anything else you want to think of.

While we are wondering about that, lets look at dentists and median age.
And you can look and look, and you will discover almost NOTHING. Dentists per capita and median age seem to be unrelated. At least my points aren't all bunched up! However, there is still a relative effect, since dentists seem to be scattered around all ages and doctors are concentrated with older people. So that might explain a bit of why the doctor/dentist ratio is not linear.