Every summer, as you well know if you have grown any kind of squash, the fruit can sometimes develop a mushy, soft, rotting spot at the blossom end.
There are two reasons that this happens:
Reason 1. The fruit develops a disease that is similar to tomato blossom end rot which happens when the water given to the plants is uneven which creates a calcium deficiency. This can be prevented by mulching to keep the soil moisture even, and by watering regularly to give the plants adequate water.
Reason 2. The second reason is that the flowers themselves develop a fungus and rot back into the fruit. This happens especially in areas or gardens that have high humidity, or where gardens are watered from above and plants are kept wet for long periods of time.
In either case mentioned above, the answer to the problem is super easy:
Simply remove the flowers once the young fruit has begun to swell and grow.
Plus - after you remove the flower, if you see any decay starting, take you fingernail and gently scrape the end of the fruit to remove any decaying material.
A small scar will form where you did this, but the rot will stop and your squash will develop into mature fruit with no further problems.
For more summer squash growing tips, make sure to read:
Growing Summer Squash - a complete growing guide