Zenker diverticulum is an abnormal pouch that occurs in the esophagus of elderly patients and can lead to aspiration pneumonia, which may present as diminished breath sounds. The patient likely has a chronic wet-sounding cough that is not necessarily a complication but a symptom of the disorder. Abdominal pain, distention, and frequent episodes of bloody diarrhea are not associated with Zenker diverticulum.