Genetic complications

If you're writing this kind of story, the main problem is the further down the line you go, the thinner the gene-pool gets. Breeders often inbred horses, dogs, cats, and various other animals to bring out a desired trait for shows and such. Maybe its a specific coloring or shape or other identifying characteristic, but after so much inbreeding, some genetic defects are bound to trail along, so these specifically bred species are more prone to infection and disease, amongst other health problems.

Granted, you won't start seeing any major complications for a few generations, but the longer it goes on, the higher the probability it'll happen, and that's something you gotta keep in mind. I'm not an expert on the subject myself, so I'm probably missing something important. Main thing is to not drag it along too far, or do some research on the subject depending on how far along you want the characters to keep inbreeding with eachother.

Now I'm not 100% sure on this, but I've read a topic on a story that dealt with an issue of **** because of an agegap between the characters in question. The main guy had an ancestor several hundred years back who had a daughter, who in the story was sealed away until the present time. At this point, even though she was his great-distant aunt, there was a guy in the forums saying that the main character is so genetically different from her that at that point it couldn't really be considered "****". In theory, the genetics aspect of this statement seems valid, but I wouldn't quote me on this.