These are the known ailments or injuries in the Warriors books.
Cough: A regular cough; what a cold would be to a human. Dangerous to elders and newborn kits.
Greencough: Similar to pneumonia. Often deadly; symptoms include coughing, wheezing, pus dripping from eyes, sneezing, and fever.
Whitecough: A milder version of greencough.
Blackcough: A very severe version of greencough, this disease is always deadly.
Chill: A very mild sickness. Like whitecough, but instead of fever, chills.
Cracked pads: The paw of a cat becomes cracked from dryness or cold.
Aching joints: Arthritis in cats
Poisoning: Poisoning from deathberries, Twoleg junk, etc.
Of course there's also the classic starvation, freezing, etc., but I shouldn't have to mention those.