So here's some of what I found:
Tight calves can cause anterior or frontal 'shin splints'. This occurs when tight calves cause an overstretch of the anterior tibialis—see illustration above. Overstetched muscles become weakened and inflammed. A heavy stretching program for the calf(ves) can alleviate the condition rather quickly.There's much more detailed information than this through that link. It explains why they're caused and what you can do to prevent or alleviate your legs when you get shin splints.
Running Injury Free
Has some good tips about how your feet should hit the ground for training purposes and for injury prevention purposes,
Sports Inury Clinic
Has some really good information for treating shin splint pain.
For me, I think my problem might be my shoes. I have flat feet so that when walk my feet tilt in towards each other. When I wear shoes with proper arch support, my feet tilt out so that the soles on the outside edges of my heels wear out (just look at my dansko clogs!). This is also called "overpronation". Can you tell I'm completely fascinated by how our bodies work?
Anyway, I either need to get different shoes or figure out an insole that I can use in them. I should probably also figure out a better stretch routine before I run. I usually only do a couple of quick stretches, but if I'm going to increase my workout intensity, I probably need to be doing a bit better for myself.
Look forward to the post about running stretches!