Melech HaMoshiach Shlita has a discussion on the Noah flood story. Truly, it is the most problematic of the entire Chumash. I am compiling a list of the miracles required to sustain the story. Grant that these are miracles. We are not exploring whether to believe or not believe. Please feel free to add any that I do not mention or dispute mine.
1) Fitting the number of animals in the space available.
2) Relying on two specimens to sustain the species and yet housing predators and prey on the same crowded ship (Mefarshim deal with this)
3) The mechanics of feeding the animals and caring for them for a year. How did they move around, clean the excretions (presumably by seeping them through holes in the second level) etc.
4) How did the ark sustain the weight of all of those animals, their provisions and their excrement for a year (Rashi says the 3rd level was for excrement. Why didn't they just sweep it overboard?)
5) The ark design is not seaworthy. It would have capsized or broken apart. It had no rudder, no keel, etc. It was just a box (Hebrew: Taivah).
6) How did the uniquely Australian animals get to and from the ark?
7) Where did they store all of the provisions for the people and the animals? It would have to be secure from the animals.
8) Every single one of the animals had to survive, since they would be the only specimens of their kind left. Even though they were abruptly removed from their normal habitat and living in terribly crowded zoo conditions, they all survived, even the most delicate species.)
9) Every current species and variation must have been represented (unless we believe in evolution, Heaven forfend). We can dispense with insects, mice and vermin though, as the Torah worldview allows for spontaneous generation.
10) A flood covering Ararat would have been over 3 miles high. There isn't enough water in the Earth system to do this globally, without resorting to some radical tide theories.
11) There are higher mountains than Ararat where people might have survived. According to pshat, the flood only went 15 amos above the peak of Ararat. (Granted, it would have been difficult to survive at that air pressure and temperature for any period of time in those days.)
12) How did the animals survive afterward with no exercise for a year? Their muscles would go into atrophy.
13) The water pressure of 3 miles of water left no geological evidence.
14) Radical temperature and climate changes for a full year did not wipe out the sea mammals, sharks and other near surface sea creatures, assuming that they did not need the ark. (Heartier than the dinosaurs?)
15) How did they provide the amphibeans access to their habitat on the ark? (Crocodiles, alligators etc. would need both water and land to survive.)
16) Getting elephants, rhinos, and less agile large creatures off of the mountain must have presented a challenge.
17) Presumably, they stayed with the ark since they could not move all of the provisions frequently as the water receded. Yet, once the water receded enough for them to populate the Earth, they were on a mountain 3 miles high. The climate would have gone extremely cold and the air extremely thin in a short time. Again, all animals had to have survived.
18) All animals had to be sound reproductively, yet they seem to have come on a random basis, not verified for their reproductive ability. There were no barren animals. They also must have successfully reproduced after the flood, each and every.
19) The air inside the ark must have been extremely stale and thin as it was used far faster than it could be replaced. There was a single window. Otherwise, it was closed and fully watertight, according to the pasukim, even above the water level. To make matters worse, they were transporting all of the excrement as well as the animals. Logic would dictate that they would have suffocated.
20) The second level, where the animals were housed, was not high enough to accomodate some animals. (The chumash does not require this, but it is commonly accepted pshat.)
21) After the calamity, the Earth was immediately productive for growing again. It must have replaced provisions in a timely manner as animals repopulated the Earth and traveled around.
22) The predators must not have returned to eating prey as long as the animals were repopulating the Earth. Then, the Earth must have provisioned them with vegetation, despite the calamity.
23) The digestive systems of many animals had to have been altered to accomodate digesting and processing only vegetation, while maintaining substantive nutrition. Then, they had to change back at some point well after the flood, to give the prey a chance to repopulate and survive.
24) Lots of germs (endemic to various animals), no illness.
25) There was no method of steering the ark over thousands of miles, but they arrived at the highest point of Ararat (Northeast corner of the known world) just as the water receded to reveal it.
26) A bird flew for seven straight days. Is this possible? Anyone study this?
27) The building of the ark is very detailed, and it had one single ingress/egress point (implied by Noah checking as they entered). Yet there was no passage between the levels. How did the people feed the animals?
This should be enough to begin. I call the bed on the opposite end from the skunk couple though.
I also pose the question: What difference does it make to living Torah Judaism if this story is literal or allegorical? Why is it so important to say that it is literal? This is not meant rhetorically. It is a doctrine (hashkafa) question.
The Godol adds the discussion on http://www.talkorigins.org/faqs/faq-noahs-ark.html.
There are a few here that are not there and visa versa.