There are several risks from just the consuming of wildlife, including choking and infectious disease. In addition to the consumption of wildlife, the dangers presented to your cat and your family from the cat's hunting include all the diseases which rodents, birds and reptiles in the wild might pass to your cat which your cat can suffer from, and, some which your cat can then pass on to your family.
- Hantavirus: cats can spread it to your family from hunting and eating rodents. "cats and dogs can spread hantavirus to humans if they bring an infected rodent into a home or other buildings where people live or work."
- Leptospirosis: "Cats typically come into contact with the leptospira bacteria in infected soil or mud, from drinking or being in contaminated water, or from coming into contact with urine from an infected animal."
- Rat-bite fever. "Rat Self-Defense: If your dog or cat gets scratched or bitten by a rat, he's at risk of getting bubonic plague, tularemia and although rare, the monkeypox virus that's similar to smallpox. But the rat doesn't have to have a specific infection to spread a disease through a bite; the rat's normal flora in their mouths and noses can carry a bacteria that causes a disease known as rat bite fever in dogs and cats. Fortunately this disease is rare in the United States."
- Choking hazards from tiny bones, broken bones or from gulping down large portions of flesh.
- Thiamine Deficiency from eating raw fish: "Destruction of B1 by thiaminase present in some bacteria and in certain types of raw fish (cod, catfish, carp, herring, etc)." In general raw meats are a bad idea for your cat: "Raw meat and raw fish, like raw eggs, can contain bacteria that cause food poisoning. In addition, an enzyme in raw fish destroys thiamine, which is an essential B vitamin for your cat. A lack of thiamine can cause serious neurological problems and lead to convulsions and coma."
- E. Coli. "Animals can carry E. coli O157 and shed the germs in their stool but still appear healthy and clean. The germs can quickly contaminate the animals’ skin, fur, feathers, and the areas where they live and roam. Animals can appear healthy and clean but can spread E. coli O157 to humans or other animals."
- Salmonella, "Animals known to commonly spread Salmonella to humans include ... Rodents (mice, rats, hamsters, and guinea pigs)." Like E. coli, salmonella is zoonotic and if it can be passed to humans, it can be passed to your cat. Other animals include bird, reptiles, etc.
- Fleas and ticks and all the diseases (e.g. tapeworm with fleas, Lyme disease and cytauxzoonosis with ticks and anemia with both) which parasites carry with them. "Pets with fleas may develop anemia, tapeworms or intense bouts of itching (pruritus)."
- Rabies (if an infected animal bites your cat)
- Secondary poisoning from rodent poisons
- Bubonic plague. Yes this sounds outrageous, but as recently as the Spring of 2016, "A feral cat that tested positive for bubonic plague." "20 humans have contracted plague in CO in 11 years" and later that same year in the Fall there was another: "a common house cat is suffering from a disease that has wiped out millions throughout history -- the bubonic plague. " In 2011, "a pet cat and a dead squirrel tested positive for the bubonic plague."
See this answer to the question, "How can cat owners protect cats from secondary poisoning from rodenticides?" for some of the dangers inherent to an outdoor cat's lifestyle. The answer references the article, "Indoor Cats vs. Outdoor Cats" by the American Humane Society which covers health, safety and environmental concerns as well as how to keep indoor cats happy. They make the point that:
A cat’s prey drive is so strong that even well-fed cats may naturally enjoy hunting birds or other small animals.
...so as a responsible cat owner, it is part of your life that you get to:
Provide your indoor cat with a variety of different interactive toys to keep them physically and mentally stimulated.
...and this can help to satisfy their hunter instinct.
If you have a cat whose job is to hunt rodents, consider the dangers, take precautions with your family as the cat will likely become inoculated and a carrier of zoonotic diseases, and, know the warning signs to look out for in case you cat does become infected. See the artciles "Is It Safe To Let Your Cat Get Rid Of Mice? The Benefits and Risks of Allowing Your Cat to Hunt" and "Warning Signs Of A Sick Cat: Issues that Could Mean Your Cat Is Sick".