For the last month or so I've noticed that the cabinet where I keep my dishes smells like mildew/mold. I just figured out it is coming from the bottom of my dishes, where it's not glazed. Has anyone else heard of this problem? I'm not comfortable eating off them anymore. They aren't that old, maybe 2 years.

Make a 1:3 ratio of fresh bleach and water. Let each dish soak in the mixture for a few minutes and allow to air dry. It should fix your problem. I'd check the shelf too because it can also be contaminated.