The problem is that any species, has a minimum viable population to avoid a pileup of inbreeding related diseases. So far the lowest possible number for human MVP is 80 people, that was an estimated number to start a space colony, with algorithms and shit helping guide breeding habits. As far as I can tell post flood Noah had a breeding population one tenth that size. Then we have to talk about the animals whose MVP are in the thousands, and this two by two shit would end in the extinction of every animal.
That doesn't even touch the issue that there isn't enough water on earth to cover the earth in water in the first place. Best case scenario it's a story of a guy who survived a local flood with his family, and then went on to reproduce with other tribes unaffected by the flood. Occam's razor has a more sensible solution than that though.
I'm only going to touch on one issue here.
I too used to get hung up on the whole repopulating the earth without inbred diseases and such. Then I heard an interesting theory that goe something like this:
When God created Adam & Eve, they were perfect in every way until sin was introduced. This muddied the waters but not to that great of an extent because they were still literally from the hands of God. So you have these near perfect individuals procreate and their kids are near perfect as well; just not as perfect as mom and dad; and so on and so on.
Noah was from Adam's lineage, while the rest of the world which was destroyed by the flood was more from Cain's lineage which was more contaminated by sin since it is never mentioned where his wife came from.
So Noah and his family may not have needed the magic number of 80 since his bloodline was more pure and hadn't had time to be completely diluted by the sin of man.