Factual error: At the very end of the film Bruce is reporting on a drive for blood donors, and Grace leads him over to the booth to give blood himself - he is even wearing a tourniquet. However, he is supporting himself on a walking stick - he is not fully recovered from the injuries he received when he was run over, which happened when he was hit by a moving car - injuries which left him clinically dead. There is absolutely no way that a person who has suffered life threatening injuries and has undergone the (inevitably) intensive drug therapies and surgical procedures involved while under treatment in hospital in the fairly recent past would be allowed to give blood. There is no way that the Red Cross (or the US equivalent) would want to encourage people who have recently been hospitalised to try to give blood. Not only would that be the height of irresponsibility, they would be wasting precious resources and staff time turning away people who would not be allowed to give blood.
Factual error: In the scene where Neo is shot at by the French guy's henchmen, they shoot with different types of guns. 4 of these are submachine guns which would fire 9mm. Another is a M1928 Thompson would fire .45 APC. Lastly there is a Heckler and Koch G36K which would fire the drastically different 5.56x45mm NATO. When Neo stops the bullets, they are all 9mm Parabellum rounds.
Factual error: The geodes occurring in the mantle during the film are impossible in two ways. Firstly, there are no gaps at those depths. The pressure is approximately 3.5 million times surface pressure, and it is not feasible that such structures could form, let alone be maintained. Secondly, the crystals inside the geodes are described as amethysts. Amethysts are a purple variety of quartz, and as any undergrad geology student could tell you, there is no quartz in the mantle, it simply is not stable at such high temperatures.
Factual error: When the Ranger trainees first meet Samuel L. Jackson, he's wearing the rank of a Specialist on his collars even though he's a Master Sergeant. Title 18, Chapter 33 of the US code prevents the unauthorized wear of a military uniform (among other things), however this does not automatically correct the mistake since a common misconception is that one slight alteration is sufficient to make the uniform legal. Having the wrong rank on is too obvious of an alteration, especially for anybody who has spent more than a day in or around the Army and would still be punishable by law, if he was dressed in an attempt to fool your average citizen outside of a movie.
Factual error: Helicopter rotor blades do not unfold by themselves and there is no way to unfold them from inside the helicopter. A trained mechanic with the right tools and equipment (including the proper ladder for the job) will take a minimum of twenty minutes to rig a four bladed rotor, and that's if (s)he's in a hurry. An airborne (i.e. falling) helicopter? Forget it. (00:07:40)
Factual error: In the movie Burke states that none of the computers has a floppy disk drive so that no information can be copied and smuggled out, but Leila uses a USB device. With all their technology and computer scientists, the CIA, or anyone who is semi-computer knowledgeable should know that information can be copied through the USB port and they would have been secured accordingly.
Factual error: Sarah Polley is dying of cancer. She's not told anyone, and the film is about completing her list of things to do before she dies. There's a scene where she's talking about children with her neighbour, a nurse, the woman who she eventually 'sets up' to replace her, to look after her husband and children, when she's died. The nurse refers to a truamatic incident having nursed Siamese twins in hospital, who both die. She describes how one died before the other -the boy, then the girl. This is medically impossible, as Siamese twins are always the same gender.