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Lots of things could be chewing the leaves. Look closely, especially at the undersides, see if you can spot the culprit. If you have lots of big holes in the leaves and you don't see anything in the daytime, come back late at night with a flashlight and check again, it might be slugs.
The black spots are most likely some kind of fungal disease.
Re what to do.... if the damage isn't real significant and isn't threatening the immediate survival of the plants, one possibility is do nothing. Zinnias are annuals. They will likely be done inside a month or so anyway.