Yup, lack of pollination. Fortunately its easy to do it correctly. See the video guide. Here is a link that might be useful: Hand pollinating zucchini

More than likely those blossoms did not get polinated and if they do not get pollinated they will simply shrivel up and die. If this is happening to most of your blossoms you may need to hand pollinate.

Image by: dthrooop Blossom-end rot is a disorder of tomato, squash, pepper, and all other fruiting vegetables. You notice that a dry sunken decay has developed on the blossom end (opposite the stem) of many fruit, especially the first fruit of the season. This is not a pest, parasite or disease process but is a physiological problem caused by a low level of calcium in the fruit itself. Symptoms BER, or blossom-end rot usually begins as a small "water-soaked looking" area at the blossom end of the fruit while still green. As the lesion develops, it enlarges, becomes sunken and turns tan to dark brown to black and leathery. In severe cases, it may completely cover the lower half of the fruit, becoming flat or concave, often resulting in complete destruction of the infected fruit. Cause Calcium is required in relatively large concentrations for normal cell growth. When a rapidly growing fruit is deprived of calcium, the tissues break down, leaving the characteristic lesion at the blossom end. Blossom-end rot develops when the fruit's demand for calcium exceeds the supply in the soil. This may result from low calcium levels in the soil, drought stress, excessive soil moisture, and/or fluctuations due to rain or overwatering . These conditions reduce the uptake and movement of calcium into the plant, or rapid, vegetative growth due to excessive nitrogen fertilization. Management Adequate preparation of the garden bed prior to planting is the key to preventing BER. Insure adequately draining soil in the bed by adding needed ammendments, maintain the soil pH around 6.5 - a pH out of this range limits the uptake of calcium. Lime (unless the soil is already alkaline), composted manures or bone meal will supply calcium but take time to work so must be applied prior to planting. Excess ammonial types of nitrogen in the soil can reduce calcium uptake as can a depleted level of phosphorus. After planting, avoid deep cultivation that can damage the plant roots, use mulch to help stabilize soil moisture levels and help avoid drought stress, avoid overwatering as plants generally need about one inch of moisture per week from rain or irrigation for proper growth and development. Once the problem develops, quick fixes are difficult. Stabilize the moisture level as much as possible, feeding with manure or compost tea is recommended by many, foliar applications of calcium are of questionable value according to research because of poor absorption and movement to fruit where it is needed but many have reported that foliar application of magnesium (epsom salts) can effect added calcium uptake. Other various suggestions consist of powdered milk, crushed egg shells tea, bone meal tea, Tums tablets, etc. but prevention is the key. Some recommend removing affected fruit from to reduce stress in the plant. BER should not be confused with fruit abortion or inadequate pollination although the symptoms may appear similar. The onset of BER occurs only after the fruit is well on it's way to development while insufficient pollination problems terminate the fruit while still quite small.

Bites from the Brown Mamorated Stink Bug have caused spots and rot on some of my ripening peppers. Look up photos of the damage they do and compare. Here's a link to get you started... https://www.google.com/search?q=brown+marmorated+stink+bug+pepper&biw=1069&bih=875&tbm=isch&tbo=u&source=univ&sa=X&ved=0CCUQsARqFQoTCP2m0MuljscCFQTQgAodhzwD8Q