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.
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.