Is there enough water in, on and over earth to cover all the mountain? ─ No. If nature poured all the water on earth and in the sky into the ocean, sea levels would still be less than 300 feet. (Details)
Is there evidence of a global flood in high mountains? ─ No. Marine animal fossils have been found in rocks near the very top of Mount Everest and in other high mountains. However, the dates of high-altitude fossils do not coincide with Noah’s flood.Over 60,000 years of snow core history do not show the kind of dramatic interruption of precipitation that a global flood would cause.
Don't flood sites worldwide prove the global flood? ─ No. There are indeed thousands of sites the world over with layers of flood sediment. However, their compositions are not consistent with a global flood and their dates are not uniform. Much of the sedimentation that literalists reference as proof of a global flood has hydrological sorting inconsistent with a catastrophic flood.
How did God protect the land? ─ With total atmospheric moisture contributing a small fraction of 1% of the water needed to flood earth, the rest would have come from the breaking up of the "great deep" below earth's surface. (Gen 7:11) The rush of water onto the continents and off again would top out at about 180 MPH according to flood models. This would have removed all of the topsoil. But cinder cones made of lighter-than-water pumice pebbles, dated reliably to millennia before the flood, remain completely intact.
Could a boat that big hold together? ─ One other supposedly seaworthy boat the size of Noah's ark was built by a Dutchman. It is nearly 230 feet long, 45 feet high, and 30 feet wide. However, its hull was built out of steel covered with wood and authorities still denied the request to take it out to sea, citing safety issues.
Is life inbred? ─ Humans and animals have too much diversity to have been as inbred as ark story implies. How did eight people from one or two ethnic groups result in Chinese, Australian Aboriginal, Watusi, Pygmy, Eskimo, Polynesian, Caucasian and other types of peoples in just 4,400 years? This is quite inconsistent with genetic studies.
Why would God do a global kill? ─ Thousands of years of continuous human habitation on all major continents contraindicate a global flood and is a testament to the vast populations beyond Noah's neighborhood. Was every single human outside Noah's family deserving of death by drowning? God did not have enough preaching prophets worldwide to make that many people culpable. God would have saved Sodom and Gomorrah if there had been a single righteous person there.
The best way to resolve the Flood story problems: Consider the story to be told from Noah's local point of view. He had no way of knowing conditions around the world. Read the Hebrew word הַר (Strong's #2022) as hill instead of mountain as the KJV does when it says, "all the high hills... were covered." (Gen 7:19) The water only raised "fifteen cubits upward" and "the hills were covered." (Gen 7:20) And read words such as all and every to mean all those known to Noah and the prophets of his day. Read the word earth as land as must be done elsewhere in the Bible. For example, when
"famine was over all the face of the earth" at the time of Joseph, nobody supposes it was global although it uses the same Hebrew word אֶרֶץ for earth. (Gen 41:56) The Hebrew (Strong's #776) is translated as land dozens of times throughout the Bible.