you have blossom end rot. many causes and theories... google it or look it up on the tomato forum!

Look at the FAQ section at the top of the Tomato Forum. Lots of info.
Nothing you can really do, but it should go away as the plant matures

Yes, I agree with the above. Blossom end rot. It is also referred to as BER.

Here is a link that might be useful: GrafixMuse's Garden Spot

Give me till tomorrow and I think I can answer your question. Early in the spring I was sold a product from the local hardware store. The product was to be used on my tomato plants. I took the product home, sprinkled some beneath the plants and forgot about it. I discovered the brown spots beneath a few of my tomatoes as you did. While looking for something else in the same hardware store I asked the owner what this white substance was used for. He explained that it was used usually once a year to replace nutrience in the soil that can be washed out from too much rain. I went home and applied another tablespoon to each plant, I also looked it up on the net and found the same substance mentioned. I have the bag and its name in the utility shed so I will follow up tomorrow morning. I believe it is a type of calcium.

OK so I am getting that this is a problem that has come from too much water (rain I guess) and can be self correcting but I can also buy a calcium supplement. Is this right?

Thank you guys for ALL of your help! I freaked when I found it and it seems to be on every plant. They are all in containers so I was worried that was the problem. But maybe the containers are just being watered too much.

Good morning, yes, it appears that the soil can be leached of this nutrient. I have calcium nitrate that I purchased at the hardware store. BTW, this hardware store is one of those that you find in a small county town where the owner has been sharing wisdom for years. The web conformed his wisdon as true. BTW, calcium nitrate is only used on tomatoes. Good luck with your tomatoes and I hope he knows what he is talking about. I just reapplied this to my plants tuesday so I haven't had time to see that my problem is solved.

Epsom salts are also used for this. I put some in the ground when I planted my tomatoes so hopefully I won't get BER. Good luck!