Regarding the TV show (possibly the comics) there are many instances where the walking dead are encountered eating their fill and one (2nd season) where one was opened up and a woodchuck was found in it's stomach. This shows the digestive tract must still work.
Where is all the zombie poop? And the smell of them must include dead food from the dead. Wouldn't it fill up their pants because we assume they did not take off their pants so neither their underwear. If one of the walkers had a colostomy bag does he have to empty it or does it fill up to his throat? If the dead have dentures, how do they chew their food?
Also, the same peristaltic waves that move the food through the digestive tract are present in the esophagus when swallowing... just nit picking I know.