Deliberate mistake: When Jack and that FBI team are looking for Sied Ali in the mosque, Jack finds a burning body in another room. He is led to believe that it is Ali, because the body's clothes matched the description that Kate Warner had given him. It is obvious that the skin is badly burnt, yet the clothes are barely scorched.
Continuity mistake: When Roger Stanton is about to be arrested, just before he stands up from his desk, we can see that the screen of his laptop is completely blue, however, while he is walking away with the army men, we can see the red ACCESS DENIED message on the screen on top of the blue background. No one touched the computer during that time.