Blossom end rot; aka BER. See FAQ in Tomato Forum
http://faq.gardenweb.com/faq/tomato/

Here is a link that might be useful: tomato FAQ

Some years I get that on the earliest tomatoes, then it clears up and the rest are fine. Here it seems more weather-related than anything else. The hotter the better.

Thanks for the help. That looks like the problem. We'll try to straighten it out and may have been overwatering it. We have 7 different varieties and have very little experience growing them. The others are doing fine. This will be a good test for us. Thanks again. Linda