There are many creationists who believe that the story of Noah's flood in the Bible is literally true and accurate, and happened exactly as described, and have gone to great lengths to try to "prove" it (and try to show how geology and all other branches of science that can actually study these things are completely wrong and biased.)
Here are some of the objections that can be presented about the literal interpretation of that story.
Richard Dawkins presents in his book The Greatest Show On Earth one of the most compelling objections. There are many, many species of animals that appear only in relatively small and isolated parts of the world, and do not appear in the wild anywhere else, not even in fossil form. For example, there are tens of species of marsupials in Australia that do not appear anywhere else in the world. How exactly did they get there from the landing site of the ark, and why did they not leave any ancestors behind during the trip there? There are species of animals that only appear in the island of Madagascar and nowhere else. Worse still, there are species that appear only in the Galapagos islands, in the middle of a vast ocean, and nowhere else. And those are just a few examples. How did they all get to those places (after all, they would have had to cross mountain ranges, deserts and oceans, most of which are way too harsh for them to survive), why did they move all in group to those precise locations, and why did they not leave any ancestors behind?
(Incidentally, the fact that isolated places tend to have animal species that appear only there and nowhere else is completely in concordance with regular evolution. It's precisely what the theory of evolution predicts should have happened during vast amounts of time and speciation of isolated animal groups.)
There are, of course, a multitude of other objections that can be presented.
For instance, was the flood water salty or fresh? If it was salty, how did all the thousands and thousands of fresh water fish species survive for 40 days in such waters? If it was fresh, how did all the salt water fish species survive? And fish are but just one paraphyletic group of animals and plants that only survive in one type of water.
How did all the plants survive 40 days and 40 nights under innumerable tons of water? More importantly, what did the animals eat after the flood was over? (Even if all animals were magically herbivorous at that time, as some creationists suggest, there weren't many plants around for them to eat after the flood had destroyed all land plants.)
If there was a global flood, then everywhere in the world there should be a geological layer that shows this. It should be a layer clearly distinguishable from other layers because of it being full of organic material and fossils, in much more abundance than any other layer. There's no such world-wide layer.
The wackiest creationist theories claim that the geologic column was formed by the flood, and go so far as to claim that more "advanced" animals were able to flee the flood to higher ground than the more "primitive" ones (completely ignoring the fact that both fast and agile, as well as very slow animals, have been in abundance during the vast majority of the history of Earth.) This theory makes no sense because if it were so, the fossils should be found lined up at the edges of old, buried mountains, rather than being evenly distributed. Unless all these animals waited for a certain amount of sedimentary layers to form, then swam miles and miles into the expanding ocean, and then dived to the bottom to get buried at that precise layer.
Speaking of which, what exactly killed the trilobites? They were marine animals, after all. If all the other arthropods and fish survived the flood, why not trilobites?
There are many communicable diseases that can survive only in a specific species. This includes human-only diseases (examples include measles, leprosy, smallpox and typhus.) Most of these diseases are either removed sooner or later by the host's immune system, or the host dies from it. The disease can only survive if the host infects another individual before curing itself or dying.
This is a really big problem for the Arc story because it says that only two animals of most kinds were saved. All the others died in the flood. For those diseases to survive to this day, those two animals would have had to contract every single one of them and keep them alive (ie. not immunize themselves) for the entirety of the flood plus whatever time it took for them to procreate afterward. Then their offspring would have to procreate further in order to keep disseminating said diseases.
We are talking about these diseases surviving for years in one host before they can successfully spread. With the vast majority of communicable diseases this is a physical impossibility (because, as said, either the host's immune system kills the disease, or the host dies.)