Other than the standard colds, flu, and cancers that plague (heh) our society, what have you managed to come up with that harries the people? I'll start with one that affects dragons and wyverns, specifically:
Y'know how people have their gallbladder or appendix removed due to infection and swelling? Draconic creatures can suffer something similar to this in my world. There isn't a name for it yet, but the flame sac that sits behind the sternum and next to the heart can swell shut due to infection. Because dragons produce an alkali substance that ignites when it contacts air, they need to expel some of it regularly to make room. If they can't breathe fire, then the sac begins to swell. Symptoms include chest pains, shortness of breath, and an orange glow within the chest that slowly grows brighter until the sac ruptures. Not many have survived a rupture, but those lucky few who have aren't able to speak and have a raspy cough due to lung damage. There is no cure, but the symptoms can be easily treated with an anti-inflammatory drug and regular use of fire breath.