Answer:
Jack: The risk is passing on genetic issues. Often these things are recessive traits - meaning that the offspring has to inherit the gene from both parents. In the case of mating with close family members, the chances of picking up the genetic issue is much increased. Often these are not things you see - they are heart issues, kidney issues - things like that. It isn't until the cat drops dead at an early age that you had any idea that anything was wrong.
Hugo: It is the same risk, but it actually doesn't happen that often with humans, either. We have many goats whose father is also their grandfather and they are fine.
Hope:
I'm not definitely sure if cats and dogs work the same, but I do know inbred dogs turn out very odd for mother-son babies. One was born dead, and the other few died very young. It can lead to a lie of problems including higher risk of cancer and tumors.
Nicole:
In most cases they turn out fine. My friend found a few kittens on her porch once and took them in and they ended up making kittens which tinted out okay. Still seems wrong to me though.
OciMom:
Its called "inbreeding' and yes there can be genetic problems in deformed or dead kittens from very close inbreeding. Beset to spay your cat now if this has happened instead of letting her have kittens and maybe witnessing horrific problems.