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The common cold is the least likely differential diagnosis for a patient with pulmonary embolism because the symptoms of a cold primarily involve the upper respiratory system and are characterized by mild, self-limiting processes, such as sneezing, coughing, and nasal congestion. In contrast, pulmonary embolism presents with much more serious and acute symptoms, such as sudden shortness of breath, chest pain, cough (which may be blood-tinged), and fast heart rates.

The other conditions listed, such as right-sided heart failure, coronary artery disease, and heart valve disease, can all present with symptoms that might overlap with those of pulmonary embolism. For instance, right-sided heart failure may occur as a consequence of a severe pulmonary embolism due to increased pressure in the pulmonary arteries from the embolism itself. Both coronary artery disease and heart valve disease can also lead to cardiac complications that can manifest similarly to acute cardiovascular events, which might lead clinically to confusion with a pulmonary embolism. Thus, these conditions are much more relevant when considering differential diagnoses in the context of pulmonary embolism.