Multiple Sclerosis (MS): The combination of hyperactive reflexes (hyper patellar reflex), intention tremor, positive Romberg's test, slowness of rapid alternating movements, and inability to perform smooth pursuits suggests a disorder affecting the central nervous system. MS is a leading candidate due to its potential to cause a wide range of neurological symptoms, including cerebellar and spinal cord involvement.

Cerebellar Ataxia: This condition could explain the intention tremor, slowness of rapid alternating movements, and difficulty with smooth pursuits. It often presents with ataxia, which could also contribute to a positive Romberg's test.
Vitamin B12 Deficiency: A deficiency in vitamin B12 can lead to subacute combined degeneration of the spinal cord, causing symptoms such as ataxia, hyperreflexia, and positive Romberg's test. It's a treatable condition and should be considered.
Spinocerebellar Ataxia (SCA): This is a group of genetic disorders that affect the cerebellum and sometimes other parts of the brain, leading to progressive ataxia. The symptoms can include intention tremor, ataxic gait, and dysarthria.

Stroke or Transient Ischemic Attack (TIA): Although less likely given the combination of symptoms, it's crucial not to miss a stroke or TIA, as timely intervention can significantly impact outcomes. Some strokes, particularly those involving the cerebellum or brainstem, can present with ataxia and tremor.
Brain Tumor: A tumor in the cerebellum or brainstem could cause many of the symptoms described, including ataxia, tremor, and cranial nerve deficits. Early diagnosis is critical for treatment and prognosis.
Wernicke's Encephalopathy: This is an acute neurological disorder caused by thiamine deficiency, often seen in alcoholics. It can present with ataxia, ophthalmoplegia, and confusion. Prompt treatment with thiamine can reverse the condition.

Creutzfeldt-Jakob Disease: A rare, degenerative, fatal brain disorder that can cause ataxia, tremor, and dementia. It's unlikely but should be considered in the differential due to its severity.
Ataxia-Telangiectasia: A rare, genetic disorder that affects the nervous system, immune system, and other bodily systems. It's characterized by ataxia, telangiectasias, and a higher risk of cancer.
Friedreich's Ataxia: An autosomal recessive inherited disease that causes progressive damage to the nervous system. It's characterized by ataxia, dysarthria, and loss of reflexes, among other symptoms.