Rotator Cuff Tendinitis or Tear: Given the patient's age and presentation of painful range of motion (ROM) in the shoulder, rotator cuff issues are common and likely. The pain can be exacerbated by movement, fitting the description of painful ROM.

Adhesive Capsulitis (Frozen Shoulder): This condition is common in individuals over 50 and can cause significant pain and stiffness, limiting ROM. It's more likely in patients with a history of cardiac disease due to potential decreased mobility.
Osteoarthritis: Shoulder osteoarthritis can cause pain and stiffness, especially with movement, and is more common in older adults.
Bursitis: Inflammation of the bursae in the shoulder can cause pain, especially with movement, and is common in this age group.

Myocardial Infarction (MI) or Cardiac Ischemia: Although the pain is localized to the shoulder, cardiac conditions can refer pain to the shoulder, especially on the left side but can occasionally be on the right. Given the patient's cardiac history, it's crucial not to miss a potential MI.
Pulmonary Embolism: While less common, a pulmonary embolism can cause referred pain to the shoulder, especially if the embolism affects the lung's pleura.
Thoracic Aortic Dissection: This is a rare but life-threatening condition that can cause severe, tearing chest pain that may radiate to the back or shoulder.

Pancoast Tumor: A type of lung cancer located at the top of the lung that can cause shoulder pain due to local invasion of the brachial plexus or ribs.
Referred Pain from Abdominal Pathology: Conditions like gallbladder disease or peptic ulcer disease can rarely refer pain to the right shoulder.
Polymyalgia Rheumatica: An inflammatory condition that causes widespread muscle pain and stiffness, often affecting the shoulders, but is less common and typically presents with more systemic symptoms.