There are a few things that need to be said in an overview sort of fashion before I dive in.
The mantra of the student of the Bible is "context, context, context..." It's always important to remember to look at the context before criticising any Bible passage. One of the most important contexts is the somewhat obvious and overlooked fact that what you are reading is part of a book that's about "God", and all that entails.
I've heard it said many times that if you can believe Genesis 1:1, the rest is easy. Indeed, one of the most important things to remember about just about anything you read in the Bible is that this is the story of a being supposedly omnipotent, omniscient, and completely good. The question should rarely be, "How could that have happened?" but occasionally, one might be fair in asking, "Why would something else not have happened?" While I don't know that one can effectively second-guess God, I don't think it's wrong to intellectually question things that God does. That's straying from my main point a bit, but it's important because I don't want to fall into the pattern of "God said it, I believe it, that's all there is to it." There is a level where a Christian has to just accept, but if you aren't a believer in the God of the Bible, this will be wholly unsatisfying; and even as a believer, one runs the risk of committing intellectual suicide, which opens the door for many things, most notably heresy.
Getting back on track to the point I wanted to make at the beginning though, there are more than a few moments in the Bible where something absolutely bizarre happens, and a casual unbelieving reader is likely to shake their head in disbelief. One of the biggest ones in the book of Genesis is actually the story of Noah, which I have had various skeptics point out to me as a story that's physically impossible on numerous levels. Frankly, I think Bible believers largely miss the absurdity of the story, and envision it as a simplistic children's Sunday school tale, with a cute little boat having animals standing two by two on the deck with smiling faces--and invariably giraffes with their heads stuck through a window towering over the rest. Well, that's unkind of me, but I do think many people simplify almost to that level, when truthfully the logistics are a nightmare. The thing for the skeptic to remember is that this story is one of the works of God.
The Bible reads a lot like science fiction in a way, especially to the non-believer. It's my view that in a good science fiction story, the reader is often presented with a specific item about which to suspend their disbelief, and after they've done that, the story should flow naturally. In the movie "The Terminator", the item is that a cyborg has been sent to the present from a nasty dystopian future. If you can buy that, the rest of the story makes sense and flows pretty well. In the case of the Bible, whether you believe it as true in real life or not, you have to accept that this is a story about "God", a being as described above. Once you accept (if only for the sake of following the story) that there is a "God", the rest should make sense. Thus when we come to Noah, the answer to most of the problems comes down to, "God did it." Maybe you don't buy that God exists, but you need to accept it as a major part of the context of the story for it all to make sense.