Pick and discard catfaced fruit. This problem should take care of itself as the weather warms. Dark, sunken spots on fruit is anthracnose and can be controlled with copper. Tobacco mosaic can be transfered to plants when smokers touch them. Don't smoke in garden, and wash hands before working with plants.
Some gardeners recommend dipping hands in milk.
Try this recipe for Fried Green Tomatoes . At the end of the season, take down cages. Pull out plants, and put in the trash. Next year, plant your tomatoes in another part of the garden. Crop rotation discourages diseases.