You Still Need to Feed Them
Cats have a predatory instinct which helps them to hunt, and they play or practice chasing prey from kitten on. What people don't always realize though is that cat moms teach their litters to kill and eat their prey. So a domesticated cat can spend all day chasing mice outside and still starve. If your neighborhood cat seems underfed, please contact your local authorities for assistance.
They Impact Local Bird and Rodent Populations
While this is great news if you have a mouse problem on your farm, neighborhood cats can harm entire populations of local or migrating wildlife. One simple fix for this is to get your cat a break-away collar with a bell. These bells give your cat's prey an extra few seconds to escape.
It is important that your cat's collar has a safe release or "break-away" feature. This safety feature will help to prevent neck injury or strangulation if their collar gets snagged on a tree branch.
Illness and Disease
Depending on the climate and on the year fleas and ticks are either a big deal or a general precaution. Natural options do exist like diatomaceous earth applied topically, but medications from your vet are the most effective. In addition to being uncomfortable for your cat and maybe you if they spread these pests indoors, some mites run a high chance of carrying disease.
Cats are capable of spreading Feline Immune Deficiency Virus via saliva. Outdoor cats that are social with other cats run a higher risk of contracting this illness. If you know your cat has it, you must keep them indoors and/or away from other cats.