Corrected entry: In the scene where Jack Bauer is at the medical station giving the gun to the photographer, as the photographer leaves, Jack pulls a gun and holds it to the photographer's head. He cocks the gun manually, but when going to decock it, instead of pressing the decock lever, he pulls the trigger and eases the hammer down. A gun expert such as Jack would know about the decock lever, and not make that mistake.
Corrected entry: Between 7:00a.m. and 8:00a.m., Nina and Tony use a room in CTU headquarters which they both agree does not have cameras in it. They use this room to interrogate Jamie about her involvement with Ira Gaines. However, when Jack is racing back to CTU between 11:00p.m. and midnight, he tracks down the camera footage from the room, even though it had none there in the first place.
Correction: Nina does indeed know there is a camera present. It is stated that the tape was deleted (presumably by her) and she is even seen looking up at it. Jack needs his code to access the back-up copy, which wasn't deleted.
Correction: He achieved his goal and it's pure speculation about whether he did it in the 'correct' way or not.
tw_stuart