Factual error: When Lucy is on the chair traveling through time, she's in Manhattan and goes back to the time before Europeans, where there are plains Native Americans on horses. Wrong Native Americans, and they didn't have horses yet.
Continuity mistake: When Lucy breaks free from the cartel prison room and kills the fellow members we see her eating then removing a bullet she grabs a bag that is half full and begins to add more weapons and items when she lifts the bag from the table for the final time there is less than half a bag.
Factual error: When Lucy is in the Chair, traveling back in time to meet the original Lucy, she finds herself still in the New York geographical area. However, the original Lucy would have been in Africa, specifically Hadar, Ethiopia. After Lucy touches her finger, she flashes once again, transitioning from the former New York City area to the vast universe.
Continuity mistake: When Lucy is in the chair in the room with the scientists, the mob guy launch a shoulder fired missile into the room, and then the room explode, both Lucy and the scientists are hit, and then Lucy goes back in time. After that when it goes back to the room when the mob boss is about to shoot Lucy's head, the room, Lucy and the scientists are unimpaired.