--Does the dog seem healthy? Does he look too thin or too fat, and is the coat shiny or dull?
--Are his nose and ears clean and are his eyes clear?
--Do you see signs of discomfort or lameness in the dog?
--Is the dog energetic?
--Does the dog seem friendly? Does he approach you readily or is he wary of you?
--When you pet him, does he lean in for more, or does he get stiff?
--When you are interacting with the dog, does he show discomfort or aggression?
--How does he interact with other animals?
You may fall in love with a dog in a shelter who is not completely healthy. Thats fine. Make sure you know what you are getting into before jumping into a long-term commitment. The dog should see a veterinarian if he seems to be really sick or injured, prior to you making your final decision. He might be really sick and you would have to spend lots of money to treat it, or it may not be treatable.
On the other hand, lots of dogs at the shelter do have internal or external parasites, skin allergies, and dehydration or malnutrition. See a veterinarian before making the final decision, and there is no reason to reject a shelter dog because of minor illnesses.
Sometimes, if a dog is frightened and scared, he may not work in your lifestyle, it depends on what you are looking for. Look for a dog who can adjust to your life easily, if you have kids, or dont have enough time to train your dog if he has behavioral issues. The ideal dog will be interested in you and he will be friendly. He will interact nicely with your other pets and respond appropriately to your kids. When you interact with him, he will not shrink away from you, or growl at you, or stiffen and show his teeth.