Here's a few:
1. Where did all the water come from? There isn't enough water on earth to flood up to the top of mount Everest.
2. Egyptian civilisation, for which there are detailed continuous historical records, pre-dates and post-dates the supposed flood.
3. Why didn't all the fish die? Neither salt water nor freshwater fish would have survived in the dliuted saline solution resulting from the flood.
4. How do you explain the diversity of human races (african, caucasian, aboriginal etc) in just a few thousand years? Human evolution isn't that quick.