Factual error: The interior shots of the Gemini and Apollo Spacecraft show worn and dirty panels, knobs, switches and circuit breakers. The movie most likely used some original cockpit trainers, but in reality the astronauts were flying brand new spacecraft that were spotless.
Factual error: Fitch, who professes qualifications in biology, genetics and biochemistry, says that they made Sil female because she's a natural predator and so she'd be more docile. He should retake his finals. In every single species of predator on earth - every single one - the females are the hunters, aggressors and killers. The males may be socially dominant but they are the 'docile' ones. There are no exceptions - and no human DNA was used to create Sil - they used synthetic DNA based on the instructions transmitted to them.
Plot hole: If Bradley Cooper was able to "quintuple" his money every day in the market as he claims to have done, he would have been able to earn the $100k he borrowed from a loan shark within a few days, starting from $800. Alternatively, he is shown in one scene winning a pot in poker where he could presumably also make a large amount of "seed" money from gambling. There was no need to borrow such a small sum of money from a loan shark, making the entire sub-plot unnecessary.
Plot hole: The fact that a five minute timer starts after the three Cerberus codes are entered defeats the purpose of the program. If they program was made to destroy their own nuke warheads in case of a misfire you would expect them to be destroyed as soon as all three codes are in.
Factual error: Whenever the fire extinguisher is activated for a jet engine, that engine becomes inoperable. In the movie, the co-pilot first activates the extinguisher for the left engine, and 30 seconds later, for the right engine. At that point, both engines should be shut down. However, the engines are still operating (and revving up) and Whitaker even asks Margaret to apply full power, which is also audible. (00:23:00)
Continuity mistake: During his conversation with the director, while discussing his costuming, Dalton's hair changes from messy and curled to gelled up and straight.
Character mistake: When Charlie is calling out the brick count to Napster from the subway, he describes it as being "13 across, 4 high, 4 deep". The bricks appear to be 2 deep in the safe (13x4x2), so he could just be lumping two shelves together, which works (13x4x4 = 13x4x2x2). The problem is that when the camera pans down there are 3 shelves in the safe. This means that there are more than the 208 bricks that Napster announces. (01:33:40)
Factual error: The cavemen Harrier pilots are shown using the hover mode frequently. Harriers, even with drop tanks as depicted in the film, can hover for at most 5-10 minutes, as the thrust required to keep the aircraft in the air without any lift consumes massive amounts of fuel and overheats the engine, and real-life Harrier pilots are instructed never to hover for long periods of time, unless absolutely necessary. The amount of time the cavemen spent hovering (hiding out of sight in a parking garage, sneaking up on the Psychlo gunships, etc.) would have easily caused their fuel to run dry.
Other mistake: At the carnival, you can see an African-American man staring at the camera for a while. I am unsure if he is a crew-member watching over the scene, or if he is just an extra trying to get onscreen.
Factual error: A force of Russian Tu-22 Backfire bombers attacks the aircraft carrier USS John C. Stennis (CVN-74) by sneaking in under the ship's radar. This is all well and good except that carriers usually don't use their own radar, they have Airborne Early Warning aircraft (E-2 Hawkeye's) that can see much further and not give away the carrier's position (let alone the F-14s which would be patrolling too) not to mention the fleet of destroyers other ships guarding the carrier. The whole point is, the US Navy practiced and planned for such a "carrier versus Backfire" battle for years. I guess in the interest of furthering the plot Hollywood has to ignore the immense measures the USN takes to protect those multi-billion dollar assets, not to mention the 5000+ sailors that man them.
Continuity mistake: When Danny gets shot at the end of the film, his paper flies out of his hand. But the very next shot of him shows that the paper is still in his hand being held over his head while he falls backwards. In one of the following shots the paper is back on the floor, but it's on the opposite side it should have been when it flew out of his hand. It's all shown in slow motion and it's very obvious.
Revealing mistake: In the scene when the main character is in the library on the internet, she goes to a couple of websites. When the shot shows the URL up top, it is C:\windows98\mydocuments\etc.html. Instead of actually searching on the web they used a premade html page and accessed it from their computer.
Factual error: As Ben is clinging to the staircase while it is falling apart, there is a close-up of a nail being pulled out of the wood. This nail is round-headed, rather than square as it would have been over 200 years ago. It's also shiny instead of rusty, which indicates that it's galvanized. Galvanization as an industrial, metal-preservation process was not patented until 1837, and was not used in building materials until well into the late-1800s. Since the film states the staircase was made by "the Founding Fathers, " and there was no galvanization of iron nails in any industrialized nation in 1780s-1830's, this is a huge anachronism.