Stroke: The combination of right arm weakness, left leg weakness, and slurred speech strongly suggests a stroke, particularly one affecting the brain's motor control areas. The pattern of weakness (involving one arm and the opposite leg) could indicate a lesion in the brainstem or a strategic area of the cerebral hemisphere that affects motor pathways.

Multiple Sclerosis: This condition can cause a wide range of neurological symptoms, including weakness in different parts of the body and speech difficulties. However, the pattern of symptoms would be less typical for a relapsing-remitting course.
Brain Tumor: A tumor in the brain could cause localized damage leading to the described symptoms, depending on its location. Symptoms might progress more slowly than in a stroke.
Encephalitis: Inflammation of the brain can cause a variety of symptoms, including weakness and speech difficulties, but it often presents with additional symptoms like fever, confusion, and headache.

Subarachnoid Hemorrhage: Although the symptoms might not perfectly align, a subarachnoid hemorrhage is a medical emergency that can sometimes present with focal neurological deficits and altered mental status. Missing this diagnosis could be fatal.
Spinal Cord Injury or Lesion: A high spinal cord lesion could potentially cause the described pattern of weakness, especially if it involves the cervical spine. This would be a critical diagnosis not to miss due to the potential for rapid deterioration.
Cerebral Venous Thrombosis: This condition can present with a variety of neurological symptoms, including focal weaknesses and speech difficulties, and is particularly important to consider in patients with risk factors such as pregnancy, oral contraceptives, or thrombophilic conditions.

Mitochondrial Disorders: Certain mitochondrial myopathies can cause a combination of neurological symptoms, including weakness and speech difficulties, but these conditions are rare and typically have a more gradual onset.
Neurodegenerative Diseases (e.g., Amyotrophic Lateral Sclerosis - ALS): While ALS can cause progressive weakness, the combination with slurred speech and the specific pattern of arm and leg weakness would be unusual for ALS, which typically starts with more localized symptoms.
Vasculitis Affecting the Brain: Conditions like primary central nervous system vasculitis can cause stroke-like symptoms but are much rarer than other vascular causes.