Final answer:
A nurse should be alerted to a potential complication in a burn patient if they have a productive cough with white pulmonary secretions.
Step-by-step explanation:
The assessment finding that should alert the nurse to a potential complication in a client admitted with deep partial-thickness and full-thickness burns on the face, arms, and chest is a productive cough with white pulmonary secretions.
This finding suggests the presence of respiratory infection or pneumonia, which can be a serious complication in burn patients.
Other assessment findings may also indicate potential complications, but the cough with white pulmonary secretions specifically points to a respiratory issue.