Final answer:
Red-tinged urine in a patient receiving heparin most likely indicates hematuria, an adverse effect of heparin therapy related to bleeding.
Step-by-step explanation:
The symptom most clearly related to an adverse effect of heparin in a 63-year-old male patient receiving infusion for the treatment of pulmonary embolism is red-tinged urine. This symptom may indicate the presence of hematuria, which is a common sign of bleeding, and bleeding complications are known adverse effects associated with heparin therapy. Such a symptom should prompt immediate evaluation for other potential areas of bleeding and possible adjustment of the heparin dose.