Common illnesses in pet reptiles include respiratory infections, metabolic bone disease, parasitic infections, and mouth rot. These illnesses can be treated by consulting a reptile veterinarian for proper diagnosis and treatment. Respiratory infections may require antibiotics, while metabolic bone disease can be managed through proper diet and UVB lighting. Parasitic infections can be treated with medication, and mouth rot may require antibiotics and wound care. It's important to seek professional help from a qualified reptile veterinarian for the best care of your pet reptile.