I would guess it is powdery mildew. First signs are often leaves getting lighter or yellowing in areas, then the white spots growing to white leaves.

You should have (lesson for next year) used the Miracle Grow rather than the bone meal as you probably stressed/weakened your plants via lack of nutrition. bone meal is for use in soil, not containers and even in soil it releases a limited number of nutrients over years. For containers you want something that gives up what is has right away, before it gets flushed out of the container with waterings.

Anyway, powdery mildew is a fungus very common to plants and even in the best cases some plants are very susceptible to it. Your zinnia, dahlia, squash and sunflowers are all quite prone to PM.

In a bad year it doesn't matter what you do, they will get it, but in a better year there are certain practices that really help. Proper watering and fertilizing are two things you *must* do for overall plant health and bone meal in a container just doesn't cut it.

Avoiding wetting of the foliage when watering helps with many fungal pathogens, but PM doesn't require wet foliage to take hold which is why it is such a common problem.

Using a fungicide as a preventative on plants known to be strongly susceptible is wise. No need to use harsh, toxic chemicals either. A rounded teaspoon of baking soda in a gallon of water kills the spores on contact. It doesn't protect the plant very long, but does a nice job killing the spores before they attach and start feeding on the plant. Done regularly (1x/week)this is often enough for fungal disease free plants. Adding a lightweight horticultural oil like neem oil (add according to label instructions or 1 ounce per gallon if no instructions) helps in that the oil coats the leaves and reduces the attachment sites for fungal spores. This too is most effective applied once per week or after a heavy rain (it washes off).

Just exactly what do you mean by 'white spots'? Is there anyway that you could let us see a picture of your situation?