Final answer:
Possible causes for the drooping of a patient's face at the end of a dental appointment include local anesthetic deposition in the parotid gland, muscle spasms from prolonged jaw opening, and syncope.
Step-by-step explanation:
At the end of the dental appointment, the drooping on one side of the patient's face could be caused by a local anesthetic being deposited into the parotid gland. The parotid gland is located near the ear and controls the production of saliva. If the needle used for the anesthetic accidentally nicked a blood vessel, it could cause bleeding and result in the drooping. Muscle spasms from keeping the jaw open for a prolonged period of time during the appointment could also be a possible cause. Lastly, syncope, which is a temporary loss of consciousness and muscle tone caused by a lack of blood flow to the brain, could also lead to the drooping of the face.