When going through security at LAX a gun is discovered when officer Ethan is going through screening. He flashes a badge and security lets him through. In reality it would take more proof than just flashing a badge to convince a TSA agent that Ethan was a police officer.
When Jessica cuts the goon's arm she tells him that he will bleed 30 liters/minute. The blood flow through a brachial artery is nowhere near that much. During vigorous exercise the entire heart puts out a total of 30 L/min, but that's the sum total flow through every artery of the body. The flow though a single brachial artery is fraction of that. In addition, the goon was not vigorously exercising. At rest, the cardiac output is about 5 L/min.
When Jessica is speaking to Officer Mooney, she clearly states that five men broke into her house. There were only four men involved and a female officer (Baybeck) who was not shown until after Jessica was taken to the safe house. Only three of the four men were shown entering the home.
As Ryan drives through the construction site with the window completely rolled down mud splashes up against the car and covers the entire driver's side door as well as the windshield yet Ryan remains completely free of any signs of mud.
Ryan records Chloe on his cellphone at the pier and she tells him that he is "iresponsible, self-centered and completely childish". When he watches the recording in the truck, she never says "self-centered".
When Ryan films Cloe, she says "You are irresponsible, self-centered, completely childish". When he plays that clip, she says "You are irresponsible,
completely childish" - without the words "self-centered".
When the shooting occurs at the Santa Monica Pier, the responding officers are from the LAPD. Since the pier is within the Santa Monica city limits, the correct responding agency would be the Santa Monica Police Department, not the LAPD.
At Santa Monica Pier, Ryan was caught by Chloe when he was talking on the phone with Ethan. The cops came, but Ryan jumps off the pier and into the sea. Then we saw him coming out off the water and hiding inside a warehouse under the pier. And when Ethan is about to kill Mooney, Ryan calls him with his cellphone. Unless the Nokia 6600 were waterproofed he wouldn't be able to do that call.
When Jessica Martin clicks the wires together to make a phone call, she first has wires apart and then tapped them together to make contact for very brief seconds. This is contrary to how pulse dialing telephone systems work. In real life, you'd have to do the opposite. The wires should make contact, and then, break contact very rapidly for the number you wish to dial.
When Jessica exits the car at the end after Ryan beats up the last thug and sees him for the first time, she seems to know right away that it is him. However, Jessica has only talked to Ryan on the phone up to this point, and has no way of knowing what he looks like, thus no way of knowing for sure this is him.
Sgt. Mooney goes to Jessica's house to investigate whether or not she was actually kidnapped. He is greeted by Dana Baybeck who is pretending to be Jessica. Later when he sees the news report about Ryan, he calls Jessica's house and hears her voice on the answering machine. It is only then that he realizes the difference between the voice of the real Jessica and the woman who answered the door. However, Mooney should've already noticed the difference between the two voices because he had spoken to the real Jessica when Ryan handed him the phone at the police station earlier on. Did he forget what she sounded like that quickly?
The Nokia 6600, used by Ryan to record the video showing the kidnappers executing people supports a maximum of 176x144 pixels when recording. However the clip displayed on the phone has a much higher resolution.
The goof items below may give away important plot points.
When Jessica strangles the bad cop in the van, the chain of her handcuffs/shackles gets longer and longer: first it looks like 10 inches (25cm), but when she removes the keys from the cop's jacket pocket, her left arm is behind the seat. To do that, the chain has to be at least 15-20 inches, and you can see that clearly. (Why would cops use shackles or fetters anyway? They would use handcuffs with a very short chain.)
When good cop Mooney fights bad cop Dimitri in the walkway by the pier near the end of the movie, the face of William H. Macy's stunt double is clearly visible at least once (when he's being shoved back into the wall), and both stunt doubles are semi-clear a couple other times in that sequence.