Mouth

The most significant change to the mouth with age is the loss of teeth.  This is caused by a combination of bone loss from the jaw, which occurs with age, and gum disease.  Both result in a loosening of teeth.  While lost teeth can be replaced with dentures these are not equivalent to natural teeth.  Dentures can make it difficult to chew comfortably.  This can result in a change of eating habits and long term deficits in nutrition.

Additional changes to the mouth include a decreased level of saliva production, thicker mucus production, and a diminished sense of taste.

Esophagus

Many other people experience difficultly in swallowing.  Most often this is a result from incomplete relaxation of the lower esophageal sphincter, but it could be a result of a neurological disorder.

Other issues with esophagus include heartburn caused by stomach acid entering the esophagus through a weakened esophageal sphincter.

Stomach

The mucus membrane of the stomach thins with age resulting in lower levels of mucus, hydrochloric acid, and digestive enzymes.  This reduces the digestion of proteins and may result in chronic atrophic gastritis.

Small Intestine

The walls of the small intestines atrophy with age.  This alters the shape of the villi and reduces the surface area across which absorption occurs.  Along with the atrophy these is a decrease in the production of digestive enzymes.  Surprisingly these changes do not result in decreased rate of the absorption of digested food.

Large Intestine

The walls of the large intestines atrophy with age.  The thinning of the walls results in outpockets from the wall, a condition known as diverticulosis.

Pancreas

The number of secretory cells in the pancreas decreases with age.  This results in a decrease in the level of fat digestion.

Liver

While the liver reduces in size with age it does not show any significant reduction in the ability to perform its various functions in healthy elderly people.