Vascular Hemichorea: This condition is a common cause of hemichorea in the elderly, resulting from a stroke or vascular lesion in the basal ganglia or its connections. The age of the patient and the presentation of hemichorea make this a highly plausible diagnosis.

Huntington's Disease: Although less common in new onset cases at the age of 78, Huntington's disease can present at any age and should be considered, especially if there's a family history. The disease is characterized by chorea, psychiatric symptoms, and cognitive decline.
Drug-Induced Hemichorea: Various medications, including antipsychotics, antidepressants, and dopaminergic agents, can cause hemichorea as a side effect. Given the polypharmacy often seen in elderly patients, this is a plausible consideration.
Hyperthyroidism: Thyrotoxicosis can cause chorea, among other symptoms. Although less common, it's a diagnosis that can be easily tested for and should be considered in the differential.

Subdural Hematoma: A subdural hematoma can present with focal neurological signs, including hemichorea, especially in the elderly after a fall. This condition requires urgent diagnosis and treatment.
Infectious or Inflammatory Causes: Conditions like encephalitis or cerebral vasculitis can present with movement disorders, including hemichorea. These diagnoses are critical to identify due to their potential for severe outcomes if not promptly treated.
Tumor: A brain tumor, either primary or metastatic, can cause focal neurological symptoms, including hemichorea, by compressing or infiltrating the basal ganglia.

Wilson's Disease: Although typically presenting at a younger age, Wilson's disease can occasionally be diagnosed later in life. It's characterized by liver disease, psychiatric symptoms, and movement disorders, including chorea.
Sydenham's Chorea: This is a rare manifestation of acute rheumatic fever, more commonly seen in children but can occur in adults. It presents with chorea, among other symptoms.
Neurodegeneration with Brain Iron Accumulation (NBIA): A group of rare genetic disorders characterized by progressive neurological deterioration, including movement disorders, and brain iron accumulation.