Blossom-end rot is caused by a lack of calcium in the fruit. If the soil pH is too low, calcium is not available to the plant. Dry weather contributes to the problem.
You can also reduce blossom-end rot by spraying with a calcium chloride solution. Ideally, you should start spraying when the first green tomatoes are about the size of a silver dollar then spray once a week for three to four weeks.
Inconsistent watering encourages the problem of blossom-end rot. So, water as needed to maintain uniform soil moisture. Tomatoes need about 1 inch of water per week. During hot dry weather they may need more. Blossom-end rot tends to be worse on staked tomato plants and when high rates of nitrogen fertilizer have been applied.
While the tomatoes that are already affected will continue to be deformed, they are safe to eat. Simply cut out the bad portion and eat the rest.
For more information see: http://www.ces.ncsu.edu/depts/hort/hil/hil-28-d.html
Photo credit: Darrell Blackwelder