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I have my first two tomato plants growing like fury in the back yard. Unfortunately both plants have signs of sickness on the leaves. The first plant is an “Early Girl” and has yellow spots. The second plant is a “Cherokee Purple” and has what looks like mold or fungus. As you can imagine, these being my first ever vegetables, I’m rather keen that they make it. If you could let me know what I might be dealing with, and how to treat, I’ll be most grateful. I’m in Oregon BTW. Many thanks.

It does look like bacterial speck and powdery mildew.
Pick off the damaged leaves, make sure you wear gloves and wash your hands and tools before you touch anything else. You may have to use weekly fungicides.

https://aggie-horticulture.tamu.edu/veg ... er/leaves/

Do I see just a little webbing on the Cherokee Purple?

It may have spider mites. They hang out mostly on the underside of leaves and are so tiny that they are difficult to see with the unaided eye . What I do is stare at first one tiny speck and then another, to see if the speck moves. They are usually red. The evidence of webbing indicates that spider mites have been there for quite awhile. They are, indeed, spiders but they suck the juices from plants.

Start by hosing them down well. Figure that if you can get the pests down on the ground, they are so small that the distance to return to the plant may be too much for them.

After the plants dry, spray them with insecticidal soap. Thoroughly. Remember that the mites hide on the undersides of leaves and ... some are crawling across the soil surface trying to get back to the plants.

Hot weather is the time for spider mites. And ... plant diseases may result from the damage they inflict on plants.

Steve