Blossom end rot can be identified by a discoloration, which looks water-soaked, or a black spot on the bottoms of tomatoes. It can also appear on peppers and eggplant. The good news is that it's not a disease, but rather the result of a calcium deficiency when the fruit was forming.
Particularly in container gardening, the calcium deficiency that causes blossom end rot is often caused by inconsistent watering. If the soil gets too dry, the plant isn't getting the calcium it needs to produce for healthy fruit. If the plant gets too much moisture the same thing can happen.
I have had blossom end rot in some of my Earthboxes, which have very consistent supplies of water and just the right amount of fertilizer and dolomite, which should provide all the calcium the plants need. The only thing I can figure out is that in an Earthbox it is the result of the hugely rapid growth you can experience and that the plant can't take in enough calcium quickly enough.
If you experience blossom end rot in a grow box, mix 1/4 cup of lime with one gallon of water and pour it into the reservoir. Only do this once. This should fix the problem.
Blossom end rot can also be the result of over-fertilization during early fruiting.
The good news is that if you growing indeterminate tomatoes (that set fruit all season) and you have a few tomatoes with blossom end rot, it doesn't mean that all your tomatoes will be affected. Even without treatment, some of your later season tomatoes may be fine.
To prevent blossom end rot:
Don't plant tomatoes in cold soil
Don't over-fertilize, especially with high nitrogen fertilizer
Don't under-fertilize. Tomatoes are heavy feeders and potting soil, unless it is pre-fertilized doesn't provide the nutrients tomatoes need.
Use high quality potting soil that drains well
Use good watering practices. Don't let your tomato plants dry out. Keep the soil moist, not wet
Add dolomite or lime to potting soil when planting