These animals can suffer from a variety of diseases, mostly resulting from improper husbandry (diet, lighting, temperature, substrate, etc.). These diseases are most commonly manifested as respiratory, gastrointestinal or dermatological problems. Call us if your snake is not eating (while snakes and reptiles do not need to eat every day, there are extremes that can be related to husbandry or to illness), if you see discharge from the nostrils, redness/sores around the mouth, changes in skin/scale color, or inability to use one or more limbs.
Fun fact: You should ALWAYS wash your hands before and after handling reptiles and amphibians. Residues on your hands may cause problems for them, and reptiles and amphibians can easily transmit Salmonella to you.