could be what nimrod or mausermeister said.... BER is likely.... but also, if you aren't getting enough pollinating insects, the fruit could be rotting because they never got pollinated. You can do that by hand by picking a male flower (no fruit at base of flower), pull off the whole petals, then rub the pollen in the center of a female flower (has the fruit attached to the base). Do it in the mid morning when the flowers are open.
If it's BER then don't over or under water. Uneven watering is said to be the main culprit. BER is actually caused by lack of calcium getting to the end of the fruit, and some will say to supplement the soil with calcium, but inconsistent watering is the main cause of the maldistribution of calcium.
I don't grow summer squash but I get BER on a few of my tomatoes in the early season, and they outgrow it later in the summer. I never water my tomatoes - let their roots go deep into the clay and they are supplied with water for the season.