Corrected entry: When Lucy races to the airplane's ladies room, she doesn't have her handbag, but she opens her handbag to take some of the synthetic drug as her body starts to fall apart.
Corrected entry: When Lucy escapes from the room she was chained in, she doesn't have the bullet that is shown in the next scene in which she shoots all the men in that room, and no one shoots her, but then she sits down, digs a bullet out of her shoulder and eats the sandwiches on the table.
Correction: She does get shot - one guy gets a shot off.
Who got the shot off? Because no one in the room she enters ever shoots at her, as they were all caught off guard.
Corrected entry: When Lucy is disintegrating on the plane, she consumes the last of her bag of CPH4. The case is open to reveal 3 and a half bags, when only 3 bags were saved. (00:54:35 - 01:10:15)
Correction: When Lucy is disintegrating in the airplane toilet, she pours a large dose of the drug from the bag into her hand, then drops the rest of the bag with drug still in it onto the floor, while she ravenously consumes what was in her hand. This is the same bag that the doctor who drugs her after the airplane gives to Del Roy. It is significantly less than half full, but there is still some drug there. This is what is in the case as the fourth bag when she opens it at the university. You can see that the drug bag has considerably less drug than the other three and is less than half full.
Corrected entry: Originally, there are four blue bags. Lucy eats the remainder of her bag, which leaves three bags. When Lucy needs all of the remaining blue bags to go into IV infusions, they put up four when it should have been three.
Correction: She does not eat the entirety of her package of drugs on the plane. While she is in drugged sleep after the airplane, you see the doctor hand Del Roy a package with some of the drug still in it. Later, when the case is opened at the university, there are three full bags of drugs, and one that is about a quarter full. That is what remains of hers.
Corrected entry: When Lucy begins to travel through space and time during the climax, she's physically appearing in the difference places - both the native Americans and "Lucy" the ape react to her appropriately with shock. but when she appears in Paris, New York, etc. in crowded areas, nobody reacts to her at all, runs into her, etc. even though she's simply and seemingly magically appeared in the middle of bustling streets around dozens and dozens of people. (Especially strange in New York, when she's in the middle of a massive crowd.) Obviously done on purpose to make the scenes flow quicker, but an oddity nonetheless.
Correction: C'mon. Stranger things happen in New York and Paris all the time. In this day and age, people costumed as Spiderman and Batman could be mugging each other in an intersection, and the passersby wouldn't even give it a second glance. A woman sitting quietly in a chair on a city street wouldn't even raise an eyebrow.
Corrected entry: The gazelle that is chased and killed by a cheetah early in the movie is male (i.e. with antlers) when chased and killed but it is female seconds later when the cheetah carries it away. (00:07:45)
Correction: The instance you're referring to (the cutaways comprised of nature footage early in the film) are meant to be symbolic momentary implications of Lucy's mental state in montage form, and are not literal scenes within the context of the film. Hence, they jump around, are different every time, etc. Therefore it's not really a continuity mistake - we're just shown random shots of cheetah attacks to show how vulnerable she is in the situation.
Corrected entry: After getting her hands, and the case, all bloody after removing the bag of drugs from the dead man's belly by hand, Lucy walks out of the hospital, gets into the car, and her hands and the case are clean.
Correction: Lucy does grab her handbag on the way to the restroom.