You can solarize your soil to kill or reduce a lot of diseases and pests.

It would help to know exactly what you were growing, and what seemed to go wrong.

Also, how exactly you constructed your raised beds - how deep were they?
Did you mix in the peat/manure/perlite with the soil underneath or just pile it on top?
What kind of soil did you have before? Sand, silt, clay?
Did you have any kind of soil tests done (nutrients, organic matter, pH etc.)?

Start by contactiung your counties office of your Rutgers Cooperative Extension Service and ask about having a good, reliable soil test done so you know what that soils pH is as well as the level of major nutrients in that soil which will help you determine what might need to be put in. IOn addition you can use these simple soil tests,
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

to see what else might need be done to make that soil into a good, healthy soil that wiil grow strong and healthy plants that are less susceptible to problems.

Here is a link that might be useful: Rutgers CES

foxcrusadr and kimmsr, thank you so much for responding with such useful questions and information.

foxcrusadr, One raised bed 6'x3' has 3 eggplants and 2 broccoli plants and beets on the lengthwise perimeter. The eggplants are going gangbusters, I'm getting broccoli heads from one plant. The other is making foliage like crazy but no broccoli. I got lots of foliage on the beets, but the beets themselves were tiny.

In another small bed, I have two zucchini plants of the bush type. Part of my problem there I think is that I caged the two plants which forced the stems together in an upright position and the whole plant got tangled. Because the stems are hollow, they collapsed over the wires of the cage. I've had a lot of fruit from it, but as the plant has gotten older, stems and leaves have wilted and died.

kimmsr, I'm going to have to go out and do the tests you suggest in order to get the information for much of the points in your post. I can tell you that my soil is not clay nor is it sand. I also did not mix the peat/compost(not manure - told you I was ignorant)/perlite with the existing soil. I was working from the Square foot gardening book.

I don't think there's a worm in there. Being a transplant from the city, I'm going to have to get used to the idea of worms.

My garden, such as it is, is on the perimeter of a brick patio that is in disrepair. The raised beds are on the perimeter and I have containers on the patio itself. The reason why I'm trying to educate myself about the soil is that, while there are somethings that are doing poorly, enough is going well that I want to expand what I'm growing. I want to get rid of the patio and put in more raised beds with paths. That's a major investment so if I'm going to do it, it should be done right.

Many thanks for your answers. kimmsr, I'll go and do those tests - drainage, etc.

It sounds like you might have enough nitrogen for green leaf growth but your soil may be deficient in phosphorus, which promotes root growth as well as fruiting - hence the small beets with bushy tops and broccoli with no heads. Or it may be there but unavailable because the pH is in the wrong range. You could try a higher P fertilizer such as 12-12-12 or a soluble fertilizer with a higher middle number than the others.

You basically have almost a potting mix there, so although kimmsr's advice for tests is generally good for gardens, it could throw you off here. The soil particle test will be useless because you don't have any mineral fraction in your mix except perlite. No sand, silt and clay. Wouldn't hurt to do that jar test on the underlying soil though, along with the drainage and tilth tests. But they won't mean much with respect to the raised bed mix.

Your zucchini may have one of the various diseases or pests that attack them. I have a heck of a time with that problem myself.