I had exactly the same problem when I moved here: it's blossom end rot (BER).
Which is most likely caused by a combination of calcium deficiency and, going by your description, overwatering. Zucchinis and cucumbers may also suffer from lack of pollination (more below).
I've learned to add a bag of slacked lime when manuring in late Winter. It has helped immensely, especially considering the cost. I suggest you do that as well. Leftover lime can be used to have deep red hydrangeas.
However you should also change your watering patterns. Plainly said, you are giving your vegetable patch way too much water.
Tomatoes don't like being overwatered like you do, at all. Besides BER it makes many varieties crack their fruits, which in turn may invite assorted pests and molds. Tomatoes should be watered once or twice a week (depending on rainfall pattern and temperatures) and the watering should be deep. There are several ways to achieve this, for example by digging a bowl-sized depression every two plants, filling it water and letting it drain.
Peppers like water, but they like even more letting the soil dry up between waterings. Daily waterings should be avoided even during droughts.
Finally we get to the squash family (zucchini, cucumbers, courgettes etc). These plants love water, but in our climates will need to be watered daily only during very hot dry spells of weather. They require plenty (plenty) of organic matter to grow well.
However these plants also need to be pollinated, and pollinated by insects. If female flowers suffer from lack of pollination they will develop squashes that fail to develop properly.
You can try to attract pollinating insects by planting attractive plants in your vegetable patch. Zinnias are great, but Russian sage (Perovskia atripicifolia) is the most amazing bee and bumblebee magnet I've seen in my life. Both plants will grow in any soil with minimal care but as they both love poor soil with little water are best planted outside the beds.
Failing everything else the female flowers can be hand-pollinated with a small clean brush, but it's a very time-consuming endeavor.
Hope this wall of text helped you out a small bit.