When you keep an animal overnight, you get a stat screen that you can look at, to make sure that animal is healthy. If the animal is unhappy or unhealthy when you return him to his owner, the owner will refuse to pay you!

HEA - Health, a general measure of how healthy the pet is
HUN - Hunger, make sure you feed the pet at least once if not twice a day
THI - Thirst, really it's silly, you feed and water at the same time
HYG - Hygiene, clean the cage area at least daily
HAP - Happiness, pet the creature if you can
ACT - Activity, you can walk dogs but really the rest of the pets are on their own

Pet Vet Walkthrough

Paws and Claws - Pet Vet Review