|Have lots of blosoms, but the fruit only gets about 4|
|A few possibilities come to mind. If the baby squash are just emerging, it could be that the female blossoms weren't pollinated. This sometimes happens early in the season, before the male blossoms appear. It can also happen during cool spells when pollinators are less active.
Also, plants need phosphorous to produce flowers and fruits. You didn't say if you have fertile soil, or problems with other plants, but you might want to use a side dressing of fertilizer high in phosphorous (the middle number). Scratch it into the soil to the side of the plant's roots.
The wet scar formed when the flower detaches from the fruit is a prime site
for infection if conditions are right. Cultural techniques like not overwatering, using a drip watering system rather than constant overhead sprinkling (wet plants create a perfect environment for disease), and growing vines on a trellis to improve air circulation all will help significantly. Mulching with a layer of dry organic material, such as straw, can help reduce the problem somewhat but is not a 100% solution to this problem. Try these cultural practices and see if there's improvement.
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 soil has poor drainage. 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. Good luck!