You have leaf miners, leaf spot and possibly slugs/snail. No mold.

And to be honest with you I wouldn't bother to treat them with anything. Unless you are growing them for greens rather than beets. They'll grow away despite a few blemishes.

Yeah, bloody leaf miners. They get my beets every season. As mentioned, you'll still get a root, but the tops sure aren't too appetizing now, which is sad because they're quite tasty.

Look under the leaves and you're likely to find egg clusters at the start of the "trails".

Yes, leaf miner damage as posted on your spinach thread that showed all the eggs. Quite extensive in this case. Any affected leaves need to be removed from the plant and disposed of far away from the garden. Leaf miners are a very common garden problem. Unfortunately they are almost impossible to treat unless you catch the fly laying the eggs or shield the plants from fly access.

Dave