Yes, some small dogs have health problems, but health defects come with just about every breed, not just small dogs. It just depends on the breed of dog. For example, my dog who is a Bichon Frise comes with eye problems, but she hasn't had any yet, but eye problems are common with Bichons. Small dogs tend to live longer and it has something to do with blood circulation and the heart, but I'm not quite sure what it is.