In the flashback scene the Native Americans shown in New York City were Plains Indians not native to NY. Also they were riding horses which are not native to the New World, but introduced by Europeans.
In the wide shot when Professor Norman first begins lecturing about the brain at the 20% capacity level, the large screen behind him has displayed the brain at 15% which is never discussed in the movie. When it cuts to a medium shot, the display all of the sudden shows 20%.
When Lucy removes the drug package from the stomach of the carrier in France, her hands are completely covered in drugs. The next shot shows her and the policeman entering a vehicle and her hands are completely clean.
When Lucy sees her cells disintegrating she locks herself inside an airplane lavatory and all the airplane staff is pleading her to open the door of the lavatory. Any flight attendant would know that the lavatory can be opened from the outside in a few seconds without much ado.
When Lucy rolls up the wall and ceiling of the prison cell as if unaffected by gravity, her t-shirt is hanging in a different direction in each shot - towards the wall or ceiling - revealing the use of a rotating stage.