Anyone have any tips on preventing damping off from occurring on beet seedlings when started indoors?
Damp off on any seedlings is caused by excess moisture and inadequate air circulation in and around the plants. As such it really is fairly easy to prevent by avoiding over-watering (a chronic problem for many) and improving air circulation with fans.
It is discussed in great detail over on the Growing from Seed forum here (FAQ there too on it).
It also helps to use a soilless seed starting mix such as ProMix BX, which does not contain the damping off fungus.
Hydrogen peroxide will kill the fungus without hurting your plant, just pick up a spray bottle of the stuff from your local pharmacy (get the pharmacy grade 3%, not the 30% hair bleaching stuff).
Other than that, just pick up a small desk fan and set it to blow on the plants.
A method I used, and I read a retired professional say he had used it, is to take dry peat and sift it, use a common kitchen flour sifter, on the surface of the planting medium.