The skin layer and the inner part with the seeds were much easier to separate than I would have expected, and the inside looked dry. (The picture shows the inside part — the outer layer came right off.)

I've seen a few posts that lead me to believe that we might have blossom-end rot. My questions are:
1. Do we in fact have a blossom-end rot problem, or is it something else?
2. Will we have the same problem with every tomato from this plant?
3. If so, I have read that we should check our irrigation system to make sure that it is working consistently. Is it worth trying to fix calcium levels, etc. for this plant, or should we pull it out? We have a bunch of other kinds of tomatoes (as well as cucumbers, zucchini, herbs) in the same (large, obviously) planter, and resources are at a premium.
4. By the same token, are we likely to have the same problem with our other tomatoes? There are a ton of large, green tomatoes growing in there, and it would be really tragic not to get to eat any of them this year!

Thanks for your help!

The FAQ in the Tomato Forum (top of that page) talks about BER and that it can be internal as well as external.