NJL-the little oval leaves at the base were the seedling leaves and will naturally wither and die. No problem there. Overall, those zukes don't look too bad. The pale white splotches could be powdery mildew, a common fungal infection, and water is the main culprit, especially if it splashes from the soil onto the leaves. For starters, cut back watering and definitely mulch that soil to reduce splash. Also, you mentioned an overhanging bench seat. Poor air circulation can contribute to fungal problems...is the bed getting plenty of sun and air movement? Be careful not to handle the leaves in wet conditions.
That one leaf with the crispy edge that you said you removed looks like it could have been splashed with a liquid fertilizer and then exposed to sun; any chance of that?
There are anti-fungal products available but most, if I remember correctly, are preventative rather than curative and in any case, if it is powdery mildew, it doesn't look like an advanced case. Mulching, drying out, and hopefully some sun might take care of it. The new growth looks healthy. Give it a bit of time and see what happens. If it progresses, check back with more photos