The oldest parts of the Old Testament are remarkably accurate, but there are a few facts in my opinion that a person must be aware of if they want to start looking for proof of biblical events:
First of all, the actual time period represented by the Old Testament is immense. For example, the period between the first cities mentioned and the time of Moses is much, much longer than the time period between current day and when Jesus lived.
The oldest events occurred long before there was writing. The history of these events was recorded via oral traditions that were passed down for no telling how many generations.
Now, about the flood:
Fact: Civilization and religion first developed in what we broadly call the middle east. Towns developed in the last few thousand years. The last Ice Age "ended" roughly 10,000 years ago. Prior to and during that Ice Age (actually several events), human populations were small, scattered, and were nothing more than hunter-gatherer societies with very limited agriculture. No permanent construction skills. Warming of the climate allowed human populations to expand greatly since then along with subsequent development of technology.
Fact: There isn't enough water (by orders of magnitude) in the atmosphere, on the earth, and inside the earth to have raised sea levels above the top of Mount Everest (which would still have been the tallest point on earth 10-20,000 years ago. Was there ever that much water on earth - extremely unlikely. However, following the end of the ice age (which ended gradually) for a few thousand years, rivers were much larger and occupied much larger floodplains (which can still be easily seen) and sea levels began rising as water trapped on land in the form of ice melted and ran down to the oceans.
Fact: Almost every culture and religion has a "great flood" story. Pretty strong evidence that something big and traumatic happened.
Current popular theory: As sea levels began to rise, they flooded into previously dry basins. There are several known examples, including the English Channel. The greatest is example is the Black Sea. The most popular theories is that the global flood stories originated from this area. The area now occupied by the Black Sea is a basin, that probably always had some water in it from rivers and lakes and was probably very fertile. Hence, there were a lot of towns and villages in the region. There is strong evidence that the Mediterranean probably broke through the Bosporus and Dardanelles straits in a cataclysmic event - triggered by glacial melting and even huge rains right at the end, and flooded the basin. There would have been evidence something big was about to happen. Through divine guidance and intelligence, "Noah" probably figured that out and built a boat and survived it. Pull up the Black Sea on Google Earth and look at how big it is. Anyone stuck in a boat on the middle of it would not have been able to have seen land and could easily have drifted for a long time.
It was several thousand years before anyone could have know what the whole world consisted of. In reality, few people knew what the world consisted of 1000 miles away. Most lived their lives within a few hundred miles if that.
Personally, I'm fascinated by the reports of the Ark on Mount Ararat. I always have been since a little kid in he 70s when I remember seeing some show about it on a mystery series (I forget the name - but I bet a bunch of you watched it - they covered all kinds of topics from Bigfoot, the Amityville Horror, UFOs, etc). Supposedly, a Chinese team recently got inside the "Ark", but I haven't heard much lately so I suspect it got debunked. Wouldn't it be amazing if it were ever found up there?
Fairly regularly you can find shows on the subject on the History Channel. They are probably available by DVD if you were really interested.