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: 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.
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.
Factual error: When James jumps on a Metro train at Union Station after killing Zack, the Metro conductor's voice is heard to say, 'Red line to Shady Grove. Next station Dupont Circle.' On the red line going towards Shady Grove, the next stop after Union Station is Judiciary Square. Dupont Circle is actually the fifth stop after Union Station.
Factual error: When Burke is explaining the exercise about following the 'rabbit', in one of the shots on the ground there's a map of the world (I think it's a political map). So, the big yellow area in Europe looks very much like the Soviet Union which doesn't exist since 1991, besides, there's no Crimean Peninsula in the Black Sea on that map.