At this late stage of the season there is nothing you can or should do. Just rake up or pick up all the leaves as they fall (and pick off any that persist) and destroy. You may need to treat for fungal leaf spot (Cercospora) if it appears next season. Also, hydrangeas very commonly have black or brown spots on their stems - they are lenticels and are perfectly normal and part of the plant's vascular system.

When my sprinkler system broke, I replaced it with drip irrigation to stop overhead watering of the hydrangea leaves (and conserve water and $$). That plus disposing of browned out leaves/blooms in the trash in December, always picking up plant debris under the shrub and replacing the mulch with new mulch helped me control the cercospora leaf spots. This disease cannot be cured but you can control it, especially by not watering the leaves (water the soil instead).

Feel free to prune the worst of the leaves now (like the closest leaf to you in picture 1) but cut them at the petiole. Do not cut the stems because that is where the invisible Spring 2017 flower buds now reside in mopheads (I assume that is what yours is).

http://www.aces.edu/pubs/docs/A/ANR-1212/ANR-1212.pdf