This is the first time in the 10+ years that I've had tomatoes with problems!

This is only affecting my orange heirloom tomatoes. The plant was given to me -- I typically only buy big boy and grape or yellow pear varieties, as well as romas.

I've looked up various remedies, from mulching to changing fertilizer, which I've already done, but I am still having problems. Anyone have experience with this?

How long ago did you add fertilizer and mulch? It will take awhile for the effects to evident.

The basic reason for blossom end rot is that calcium is unavailable to the plant. This could be because the soil is compacted, not allowing water to penetrate deeply enough to feed the plant, or uneven or not enough deep watering, which will have the same effect as not getting enough water. It could be that the soil doesn't have enough calcium in it. The soil could be slightly cooler for various reasons, or the roots may have been damaged by hoeing or pulling weeds too close, or by some underground disturbance (moles?)

Heirloom tomatoes typically survive less than ideal conditions better than hybrids though, so this could be hard to track down.

I have one plant (of 28) that has a mottled appearance. I know something is wrong, but don't know what. My heirloom cherry tomatoes (orange, low acid and sweet as can be) weren't growing very well, so we finally fertilized and they are growing wonderfully. I have all heirloom this year, including two black varieties. I am not very impressed with any of the black tomatoes.