Plot hole: When Kim sees Gary she runs into the master bedroom, hides her bags, goes into the closet and up to the attic - all in the time it takes Gary to run five yards to the bedroom door. And considering how much noise the attic door made he should have heard her. Plus, how did she manage to get the door hatch closed when she had gone up?
Continuity mistake: Mike Novik is briefing President Palmer about his phone call with Jack Bauer. In one shot Mike gets so emotionally involved in his speech to Palmer, a tear roles down his face and his eyes are glazed. The camera switches to Palmer, and in the next shot of Mike, his face is dry and his eyes are not glazed anymore.
Revealing mistake: When Kate Warner phones her sister, Marie holds her phone up to the camera and you can see that the words "KATE'S CELL" have been written using the 'Write Messages' function on her Nokia. The 'abc' in the corner gives it away plus you can see the cursor trying to be hidden by being moved next to the 'K'
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: Marie Warner goes to see Reza at her father's office at about 5:30. When she enters the office, she puts her handbag on the table and embraces Reza. After they embrace she picks her handbag up from the floor next to Reza's chair. There was no time or opportunity for anyone to move her bag.
Other mistake: In the shootout at the stadium, several times when Jack fires a gun the sound of the gun firing is heard but it is obvious that the gun did NOT fire. Most noticeable when Jack fires the third shot at the man behind the wall and when he is struggling for the gun with the last guy who he beats up.
Plot hole: When Kim is brought back to the police station for the last time, the officer explains to her that they now know it was Gary Matheson who killed his wife, and that they are still looking for him. Why then, would Kim and her police escort not even consider the possibility that he might be hiding at his home when they arrive to get Kim's belongings? Even if the police searched the house once before, you would have to be insane to allow a teenage girl to enter the home of a known murderer on the loose. Beyond that, Kim herself never seemed to consider the threat.
Factual error: Invoking the 25th amendment cannot be done by vote. The members have to send in their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall then immediately assume the powers and duties of the office as Acting President.