The small zucchini that is rotting on the vine is probably an unfertilized one. There are bound to be a few during the course of the summer. Also check on your watering to be sure it is fairly steady - don't overwater. Zucchini seem to thrive with less water than you would think.

Here is a link that might be useful: Zucchini blossoms

Honestly I don't see any problems in the picture. An unpollinated fruit perhaps which is common and some over-crowding of that tangle of stems. If you have yellowing leaves it is most likely due all the rain or over-watering.

Note all the discussions running here right now on squash problems? 5 or 6 of them just below your post. They are all in the same situation as you - squash problems. Why not read through all those threads for even more information?

Dave