Thin skin in the elderly is quite a common occurrence, and Jennifer is right, it can be exacerbated by a daily aspirin, Plavix, or coumadin regimen (blood thinners) or by chronic use of prednisone for other conditions.
In addition to the loss of the fatty layer beneath the skin, one of the largest contributors to this tendency is actually chronic and lifelong accumulation of sun damage which causes breakdown of the elastic and resilient fibers of collagen and elastin in the skin's dermis layer. Additionally, these elastic fibers usually line blood vessel walls in the skin, so when sun damage accumulates, the vessel walls themselves are not as resilient, and can be more fragile, creating easy bruisability, even from no obvious known trauma.
A lot of this type of bruising (known by the nickname "senile purpura"--senile not referring to dementia, but just aging) can look scary to an outsider, but it does not mean an abnormal amount of trauma is occurring, just an abnormal response to regular everyday trauma.
In some cases, if it develops more suddenly after a blood thinner is added, the primary care physician may choose to decrease the blood thinner. Sometimes the combination of regular varicose veins in the area, and this fragile skin, can lead to more bleeding than expected. Don't be alarmed, but do call the primary physician to discuss options.
One thing to watch out for with an elderly, demented family member who may be on a blood thinner to decrease the risk of a clot, is the risk of an internal bleed that may occur due to a fall. This should also be discussed with the physician to make sure the patient is protected properly on both ends of the spectrum.