Answer: Zucchinis produce male and female flowers, and you can tell the difference by looking at the base of the bloom. Female flowers have a bulge like a mini fruit, male flowers do not. The first flowers of the year will be male, followed in a few days by female flowers as well.
Damp weather is ideal for fungal problems to develop, and you may be seeing something such as anthracnose on the zucchinis -- this would cause sunken spots on the fruit with truly ugly masses of sticky, pink spores. It occurs in warm rainy weather, can be seed borne, or can survive in the soil and on plant debris, so it is important to rotate your crops and allow adequate spacing between plants. On the other hand, they may simply be waterlogging if your garden is poorly drained. Another possibility is squash bugs have damaged them and rot has set in as a result.
In the meantime, keep removing the infected fruit as soon as you see signs of the problem. Avoid overhead watering, and replace the mulch immediately around the plants with a fresh layer. Destroy the old mulch and plant debris to try to limit reinfection.
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