Blossom end rot is a common tomato problem. According to the
UC Pest Note for blossom end rot, affected tomatoes will "show small, light brown spots at the blossom end of immature fruit". Typically, the damage occurs when the plants are water stressed or when the plants have had wide fluctuations in soil moisture, and when the fruits are about 1/3" to 1/2" of their full size. It's not caused by a pathogen, so there are no pesticide solutions.
Key recommendations are: