This is a simple one, two.
1/ Dendrochronology http://www.sonic.net/bristlecone/intro.html
Earth's oldest living inhabitant "Methuselah" at 4,767 years, has lived more than a millennium longer than any other tree.
There are trees alive that were already several hundred years old when the Flood is meant to have happened.
2/ Ancient civilisations, for example, the Egyptians http://ce.eng.usf.edu/pharos/wonders/pyramid.html
The monument was built by the Egyptian pharaoh Khufu of the Fourth Dynasty around the year 2560 BC to serve as a tomb when he dies.
The Great Pyramid ay Giza is just one of many ancient monuments that pre-date Biblical dates for a Flood yet which cannot have been standing during the Flood.
Therefore the 'global' Flood wasn' global, if it is based on any real event at all, therefore the Bible isn't an accurate hsitorical record.
Just for the record, we share LOADS of DNA with H. neanderthalis, it's just not of a nature which suggests direct decent of modern man from H. neanderthalis. Best guess at this point is modern man decended from a migration of H. sapiens out of Africa which displaced evolutionary cousins who migrated out of Africa earlier and evolved specific morphology for Ice Age environments in (mostly) Europe. This displacement may have been so extensive there was no interbreeding, although there are some claims for hybridisation or (more demonstrably) at least living side-by-side for thousands of years.
In terms of appearance H.neaderthalis would have looked freaky, but MIGHT pass for human with a bobble hat on. We don't know if H. neanderthalis was 'as' human as us (i.e. speaking and thinking as us) or whether the archaic H. sap population had a major advantage because of something like 'modern' thought and syntaxitical language which the older populations of neaderthalis lacked.
Anyone who says they neanderthalis were Nephilim is probably too ignorant to bear talking too for extend periods without your own spleen strangling you...