The building of the ark isn't even the most difficult part of the story to swallow, even if his boat was sea worthy. Here's some farther fetched aspects of it:

1. Capturing a male and female of each species, even if limited to local species.
2. The story didn't limit it to local species.
3. Flooding out even people who lived in mountainous areas would take a ton of water, not sure if even 40 days and nights of downpour would get there.
4. That big of a flood would leave significant evidence.
5. Where did all that water go after the genocide was done?
6. A lot of vegetation wouldn't survive being submerged for over a month.
7. It was a reset for all species, were the animals as wicked as the people were?
8. What did the other gods have to say about this (since the flood happened during a time before the Jews were monotheistic)?
9. It's the whole "how did Adam and Eve make the whole human race without a lot of signs of inbreeding?" thing all over again, except now for every species.
10. What did they feed all those animals for that month, especially the ones that ate other animals?
11. If the answer to any of these amounts to "magic" then why not just use that magic to do the genocide without introducing so many plot holes in a story made up in a time when few could tell it was full of plot holes? Just call down massive lightning like Sodom (and don't get me started on that story...).