Septoria leaf spot or blight will cause white spots on leaves and can occur during humid conditions when plants are so close as to have poor air circulation around them.
White spots on the fruit could be a bacterial canker, one of the most difficult problems to control. This, as you suggest, could come from the soil—specifically from not rotating. The thing is, avoidance is depent on rotating out the entire nightshade family. That includes tomatoes, but also eggplant and potatoes as well as peppers and tomatillos. You should avoid planting tomatoes, eggplant, or potatoes in the same soil, or each other's soil, for two to three years (some say, unequivocally, three years).
When you find a new spot for the tomatoes (and other crops, if you grow them), use rich compost and check the pH.
If you do all of this, kudos, but you still get the cankers, it could be that the problem originated in the greenhouse that produced the seedlings (you did not cite the origin of your plants). Elmination of an "industrial" problem involves sterilization of virtually everything, from tools to soil.
Perhaps it's not too late to get "new" soil for new plants and grow them in pots.
Septoria leaf spot or blight will cause white spots on leaves and can occur during humid conditions when plants are so close as to have poor air circulation around them.
White spots on the fruit could be a bacterial canker, one of the most difficult problems to control. This, as you suggest, could come from the soil—specifically from not rotating. The thing is, avoidance is depent on rotating out the entire nightshade family. That includes tomatoes, but also eggplant and potatoes as well as peppers and tomatillos. You should avoid planting tomatoes, eggplant, or potatoes in the same soil, or each other's soil, for two to three years (some say, unequivocally, three years).
When you find a new spot for the tomatoes (and other crops, if you grow them), use rich compost and check the pH.
If you do all of this, kudos, but you still get the cankers, it could be that the problem originated in the greenhouse that produced the seedlings (you did not cite the origin of your plants). Elmination of an "industrial" problem involves sterilization of virtually everything, from tools to soil.
Perhaps it's not too late to get "new" soil for new plants and grow them in pots.