Define 'day' as observed by God. A day is the amount of time it takes a body to rotate 360 degrees. If God measured time in days, then he was on a planet that orbits a star, and therefor Genesis is wrong in the first line, because God couldn't create anything on the first day, because there was no day.
Using the literal exegesis of Genesis as calculated by Bishop Ussher, God created the world on October 3, 4004 BCE at 9am. However, it wasn't taken into consideration that the Gregorian calendar wasn't used until 1582. Before that, the Julian calendar was used. But, due to the way it worked, 3 days were gained every 4 centuries, which threw off the equinoxes. As a result in the differences in the two calendars, January 1 in the Julian calendar is actually January 14 in the Gregorian. Also, calendars before Rome standardized them, varied by region, city or culture.
Fossils. There are many examples of fossils from creatures that existed that genesis, or the rest of the Bible, makes no mention of. In the story of Noah, God commands Noah to collect 2 of every creature. Yet, there are thousands of creatures that we have physical fossil evidence of that were not mentioned. You would think something as large as an Apatosaurus would rate a mention, at least. And, if some sea creatures, like a Sperm Whale, survived, why didn't Trilobites? And, where is the fossil evidence of all the people that were killed in the flood? If not fossils of the people themselves, the trace remains of their settlements should have been found.
Contradictions. Genesis is full of them. Example A, Genesis says that on the first day, God created light and separated it from the dark. But then it says God created the Sun on the fourth day. The Sun is what provides the light, so which is it? Example B, Birds. Genesis first says they were created out of the water, but then later in the chapter, it says they were created out of the ground. Example C, Animals. God first created animals and then created man. but later on, God created man and says it wasn't right that he walked alone, so God created animals.
These are just 4 arguments I could make against genesis. Give me a week and I could write a book disproving it.
Too bad I don't have 10 grand.