I would suppose the Patriarchs of mankind, because of their great age, likely had many many children their children had many many children as well.  

At that early stage it seems likely the genetic problems associated with inbreeding were not a problem because of the relative perfection their long lived bodies.

It wouldn't take long for such long lived people and their descendants to populate the earth.

we are more degenerate genetically and inbreeding, as such, only results in flawed issue when there are flaws to be doubled upon.

Inbreeding is usually used in animal husbandry.  The defects that result are eventually weeded out until a pure-bred is developed.  Pure-breds tend to be closely related to each other, but usually able to breed without too many problems.

Richard F. Burton claimed that Jєωs are not only longer lived than gentiles but that they are able to inbreed with fewer ill-effects.  

There are two possible explanations for this.

One is that they were selected by the rigorous enforcement of their тαℓмυdic law and by continual inbreeding to be resistant to the negative effects of it.

Another possibility is their descent from Abraham, Isaac and Jacob endows them with special characteristics that give them hardiness and keen wits.

Perhaps both are correct to some extent.

Also, I know that Shem, Ham, and Japheth represent the European, African and Asian(Middle East and Anatolian) peoples in the Old World respectively. How about the Native Americans in the Western Hemisphere and the East Asian peoples in the Orient?

You're off a bit.

Sem = Asian/Middle Eastern
Japeth = European
Cham = Black

Japeth means "expanding" which is an appropriate name for the race that has a knack for restlessly exploring, improving, and establishing global empires (Roman, Holy Roman Empire, British, French, American, etc.)

The Blacks don't explore, expand, OR invent much of anything.

The Asians, while very intelligent, don't seem to have that restless drive that sends them to the far corners of the earth. They also tend to be more conservative -- keeping things the same way for centuries.

Inbreeding is a powerful genetic selection tool when used in livestock breeding programs.  There are different degrees of inbreeding, some more severe than others.  Essentially, it concentrates the genetics of an individual, especially recessives.  It takes two copies of a recessive gene to express the trait, whatever that may be.  

Basically, both "good" and "bad" traits are concentrated.  We often utilize severe inbreeding to purify a bloodline by removing as many negative-trait-carriers as possible.  We then heavily select for prime traits.  

Most breeds were developed using inbreeding- in sheep, for example, the Leicester Longwool was developed with that method by Robert Bakewell.  

There's a general misconception that inbreeding is bad and to be avoided (in animals).  I'm sure that's due to our negative view of incest.  Sure, poor quality animals can be produced.  In particular, growth rates and size tend to decrease unless deliberately selected for.  But when done responsibly and wisely, some pretty outstanding animals with very pure and reliable lines will be produced.

I always assumed that the genepool for every species and mankind was pure in those days.  Mutations keep occuring very frequently and we have a host of genetic defects to show for it.  So a brother marrying a sister or cousins marrying cousins would be unlikely to produce children with undesirable genetic features.  The same argument could be made for the animals that were in the ark- obviously the genepool would be very small.

I find genetics and gene transcription/translation to be incredibly fascinating and complicated- something almost all of us take for granted.  It's absolutely amazing the diversity that can be obtained in a flock when a careful "conservation breeding" program takes place- using inbreeding to then try and produce several genetically distinct lines using only one ram and several ewes.  I can see a similar situation easily happening with people.