Changes in coordination are less related to muscles and more related to the brain and nervous system. Multiple brain centres need to be well coordinated to allow you to do everything from hitting a golf ball to keeping a coffee cup steady as you walk across a room. This means that the wiring of the brain, the so-called white matter that connects the different brain regions, is crucial.
Unfortunately, most people in our society over age 60 who eat a western diet and don’t get enough exercise have some tiny "ministrokes" (also called microvascular or small vessel disease) in their white matter. Although the strokes are so small that they are not noticeable when they occur, they can disrupt the connections between important brain coordination centers such as the frontal lobe (which directs movements) and the cerebellum (which provides on-the-fly corrections to those movements as needed).
In addition, losing dopamine-producing cells is common as you get older, which can slow down your movements and reduce your coordination, so even if you don’t develop Parkinson’s disease, many people develop some of the abnormalities in movement seen in Parkinson's.
Lastly, changes in vision — the "eye" side of hand-eye coordination — are also important. Eye diseases are much more common in older adults, including cataracts, glaucoma, and macular degeneration. In addition, mild difficulty seeing can be the first sign of cognitive disorders of aging, including Lewy body disease and Alzheimer’s.