Your apples have a fairly severe case of sooty blotch and flyspeck, two closely related fungal diseases. These fungi colonize the wax layer on the outside of the fruit and give the fruit a slightly musty "mouthfeel", and shorten the shelf life.
We tend to see more of these diseases on older trees with thick canopies that promote slow drying. Years with more summer rains have more sooty blotch and flyspeck.
The fungicide Captan helps suppress this disorder. Applications start about 3 to 4 weeks after petal fall, reapply after about 3 inches of rain has occurred.