A zucchini will rot from the blossom end when, due to improper pollination, the plant aborts it. This is often mistaken for BER. I don't think BER applies to squashes, but I could be wrong about that. Anyway, lack of pollination is likely the cause of the rotting zukes.
As far as what's gnawing on them, I have no idea. I've had birds peck at small, immature squashes before. But they give up after a few pecks.

Hi tcstoehr,

I'm confused and hope you can clarify. It's my understanding with vegetables that when a bloom is pollinated, then it starts growing the fruit. If the bloom isn't pollinated, then it drops off and no fruit. So you are saying that with zucchini, the female flower can produce fruit without being pollinated, yet will abort if it isn't eventually pollinated somewhere during the growth of the fruit?

the female flower already has a small fruit attached before it is pollenated. If pollenated, it grows. If not, it rots and drops off. Additionally, if the plant cannot handle the amount of zucchini's, it may abort some before or after pollenation in which case the female blooms can fall off before opening or the fruit can stop growing and rot after pollenation.

Ania