I'm in Los Angeles. The plant is in a container on my balcony, where it has to breathe LA air and get covered with LA dust.

The black crud is pretty evenly spread around, though there's less of it on newer growth. You can see it around the edges, though.

Here are some pics. The whole plant, some new growth, and some areas I might consider pruning soon. The leaf miner damage to that one leaf, by the way, is old.

FWIW, I sprayed it with neem last night. I figured that would give me some action against fungi and bacteria, and if it turns out we can identify it as certainly fungal, I'll spray with copper.

Huh. Assuming it's not just LA black dust...

Did you by chance recently have aphids? After seeing more photos, it kind of looks like it could be sooty mold from sap-sucking pests. On tomatoes, that's most likely from aphids. The rolled leaves are also a sign of sap-sucking pests, although given your location, it could just be physiological leaf roll from the heat.

Another thing it could be is atypical presentation of mite poop. Take a magnifying glass and examine the undersides of the leaves. Mites are small enough that most people can't see them with the naked eye. If they're mites, you might have to look hard, since you may have knocked them back quite a bit with the neem.

If could be fungal disease, too (as opposed to something like sooty mold that doesn't feed on the plant but rather on honeydew left by pests), but I would expect to see some yellowing of the leaf in your original post if it were.

No, no aphids. Had some leaf miners awhile back but they seem to have died off on their own. No new damage in maybe 2 months. Caterpillars, but I got rid of them awhile ago, too--though I found three small hornworms while composing the original post. (If that wasn't all of them, I'd assume the neem got the rest.)

I also don't think it's just the dust, which normally collects on top of the leaves.

Seems like the best course of action will be to see if the neem helps at all, and maybe hit it again in a week. If it's mites and the neem is killing them, problem solved. I figure it should also help with sooty mold, if that's what this is.

Dust could behave differently if there's a lot of soot from fires in the air, or if there's been any moisture on the leaves + winds, etc. The leaves that I see there that are yellowing are not doing so in a way consistent with fungal disease, and other than the possibility that the black stuff is sooty mold, and the leaf curl (which could be just from heat stress or something), it doesn't really look like pest damage. How easily does the black stuff come off?

The black stuff doesn't seem to come off at all. So now I'm pretty convinced it's not dust. Could it be some kind of nutritional problem? I feed with Tomato Tone, per the instructions on bag--works out to be about 4.5 tsps every other week.

I don't know any nutritional problems that look like that. Sooty mold on honeydew is pretty stubborn. If you haven't seen any aphids, have you seen whiteflies?

Or maybe it's just something fungal I haven't seen or that is presenting in a way I haven't seen. If the neem doesn't stop it or slow it down, copper tends to work against a wide spectrum of fungal diseases.

I haven't seen a pest on that tomato plant at all, except for the now-dead caterpillars. Hmm.

The neem seems to have helped a little, so I'll either try it again next week or switch to copper. It's already stained my sprayer blue, anyway.

Thanks, Gorbelly.

I'm curious whether the problem progressed or was controlled. Did you ever figure out what the black stuff was?

Good timing. I thought it was under control, went away for the weekend, and came back to this additional puzzle piece just an hour ago.

If I saw something like that on a tomato, I'd assume it was physical damage, i.e., something rubbing against the fruit. The sunken dot could be where it was pressed up against the cage/trellis or possibly another fruit or a stem.