Hi, everyone,

Please forgive me if you've seen this post already, and feel free to ignore if that's the case. I first posted in the Vegetables Forum, only to realize there was a dedicated Pests and Diseases Forum, only to realize there was a TOMATO Pests and Diseases Forum. At this point, I've well and truly covered my bases, and I'll be sure to be more careful in choosing the appropriate forum for future posts.
This is my first year in a house and thus my very first garden. I started late in the season, so mostly bought my plants. My patio tomato and sweet hot pepper plants looked especially happy (or so I thought) when I planted them but now something is clearly going very wrong, and I'm so clueless. I've googled until my eyes crossed and still feel too hesitant to name what on earth is afflicting them.

A little about the setup--I have a 4x4 raised bed (the patio tomato is in the bed not in a pot). I dug down about 8-10 inches and built up the sides about 6. I filled with a mix of compost, vermiculite, peat moss, and the native soil.

The problems:
The patio tomato has mottled purply brown splotches all over. I thought it was limited to one branch but it seems to be spreading. I plucked the worst ones off. You can see the pics below. My best googled guess was leaf mold, and if so, how do I treat it?
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And then I thought it was just the patio tomato, but the pepper plants looks ill as well. This wee pepper is completely covered in sooty mold.
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And the pepper's leaves have a few white and brown spots.
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I haven't seen bugs camping out on the plants. The undersides of the leaves do have some detritus that I assumed was dirt from a rather messy planting process but now I wonder if it's bug-related.

Any ideas on what issue (or multiple issues) I have? And can I treat it? I have Neem Oil around somewhere from a houseplant infestation a while back, but I don't think that's effective on fungus, if that's my problem. I'm sorry if this is all rudimentary--Gardening 101 if you will--but Gardenweb has always been so much more helpful to...