What stages in swallowing can disorders occur?

Dysphagia. "transfer dysphagia" is a problem moving the food bolus from your mouth to the top of the esophagus; "transit dysphagia" is a problem transiting the food down the esophagus. Motility studies (modified barium swallow with speech therapist; esophageal manometry) may be helpful in identifying the point of pathology, if present. Sometimes, just esophageal spasms can make swallowing feel problematic.
Swallowing problems. There are numerous swallowing disorders that relate to the rigidity of the esophagus (too lax is called achalasia with ectasis or too rigid due to scar or radiation or injury) and then there are a series of motility disorders most commonly seen with a stroke in which coordination of the movement make it difficult for food to pass from the mouth to the stomach.