All well-known brand cat food is going to have the right balance of nutrition for your kitty. You don't have to worry about health issues (unless your cat has allergies to certain foods). Now, if you live in a country where it is difficult to get name brand cat food, you need to talk to your vet about what is the best available.
You do have to worry about health issues when you feed your cat people food. Getting all the nutrition your cat needs with people food is very difficult unless your vet is guiding you every step of the way. Your kitty will likely be even more healthy if you transfer him/her to a brand cat food.
@Keshlam is exactly right that inside cats have a problem with dehydration. The wet food helps this issue, since it has a large percentage of water in it.
Your issues with feeding only wet cat food will be...(1) soft stool (that may turn into diarrhea often),(2) ensuring you take up the dish after your kitty eats (just like us, you don't want to leave wet food out all day; the food can degrade and harm your kitty), and (3) teeth problems (also mentioned by Keshlam).
To ease the issues I mention above, I feed my cats dry food during the day and wet food at night. AND I have a drinking fountain with constant running water for them, which encourages them to drink more...well worth the money.
Just some things to think about. I wish you and your kitty the best!