Those spots are a fungal disease or possibly a bacterial one. They usually don't threaten the life of a hydrangea but they do make it unsightly. You can purchase sprays for such things at your garden center to keep it in control. I find that in minor infections if I rake up fallen foliage and pick off affected foliage the problem often diminishes, provided the weather doesn't keep the plant wet for an extended period again. If you choose to spray do so right after rains to provide protection from infection.
Hope this helps.
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