Continuity mistake: When Layla is hooked up to the lie detector that tracks the movement of her eye, she is looking around the room and blinking repeatedly, but the eye on the screen (which is supposed to be hers) never moves or blinks, even though the camera is still on her.
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.
Continuity mistake: After Clayton says Burke's name to his 'captors' he is shown holding a pair of pants, in the next shot he is not holding them, then the next shot he is again.
Other mistake: Towards the end of the movie, Clayton has two wounds visible on his face. These wounds keep changing length and shape throughout the scene.
Visible crew/equipment: When James gets into Layla's car after forcing it off the road, the boom mic can be seen in the rear side window of Layla's Volkswagen Beetle.
Continuity mistake: In the shooting range scene at the Farm, the Recruit to Layla's left fires all of his rounds and his slide locks back when the camera is close up on Layla. In the next shot, the same recruit fires one last shot.
Factual error: Burke says Clayton graduated "top of your class at MIT, majored in nonlinear cryptography..." but MIT has no such major. In fact, there's no such field.
Continuity mistake: When Layla's VW has hit the tree, James's truck is pulled up alongside her, facing forwards. When James drives off, his truck is facing the other way but there was not enough time for him to turn around, or any indication that he did turn around (i.e. no sound of a vehicle making a three point turn).
Continuity mistake: When James is standing at the wall of the interrogation chamber holding Layla's trousers in his right hand, the trousers are there in one shot, gone the next and back in the next.
Factual error: In the middle of the film, as Farrel and Pacino talk in the park, Pacino tells Farrel about a new computer virus that Langley's created. He says it uses existing wires to propagate itself and can spread through, say, an electrical wall outlet. Computer viruses are programs that copy themselves (spread) when executed - this requires specific operating systems and CPUs. Anybody even remotely knowledgeable about computers knows this. The thought that a computer virus could somehow spread through the electrical grid or infect a toaster is ridiculous, since the only part of a computer actually connected to the electrical net is the PSU, and no data goes from it to the CPU.
Factual error: After Clayton kills the man in the subway, he calls Walter using a cell phone and proceeds to tell him what just happened. Two trained CIA agents wouldn't use unsecure lines to relay that sort of information, especially when they are meeting soon.