Hi and thanks for contacting Ask an Expert. The mold is just starting on your plant. You can use a baking soda based fungicide spray to get rid of it. Since it is just starting you can also wipe it off but you will need the spray as well. Take a paper towel and gently remove the mold. Fungi are everywhere and are just waiting for a chance to grow.
They need warmth and moisture. Which they get this time of year and from watering overhead. Water at the base of the plant and don't get water on the leaves. Also do not over water. You can check the moisture in the soil by putting your finger down to the first knuckle. If it is moist to that depth you do not need to water. Having a good soil mixture is important as well. Plants that have plenty of nutrients in the soil resist disease and insects better than those that don't. Your plants look very healthy other than the mold. Try to keep a good air flow going through the plant by removing the squash early and any dying leaves.
After a good harvest it is a good idea to either side dress with a dry fertilizer or add a fish emulsion to the soil. Using organic fertilizers are best, they will not burn your plants. The liquid fish emulsion will get to the roots quickly and help the plant produce more squash.
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