Final answer:
The priority for the nurse is the client's drooling during mealtime, as it poses a risk for aspiration and serious complications like pneumonia.
Step-by-step explanation:
A nurse monitoring a client with Parkinson's disease in a long-term care facility should recognize that the priority among the listed findings is when the client drools while eating. This is because drooling may indicate difficulties in swallowing or controlling saliva, which could increase the risk of aspiration and lead to pneumonia, a serious complication. The other findings such as eating habits, tremor, and social preferences, while important aspects of care, are less immediately life-threatening.