Day 3: 8:00 P.M.-9:00 P.M. - S3-E8
Revealing mistake: Right when Jack and the prisoner are walking through what appears to be the gun room in the prison, you can see the guy who attacks them through the door. You can only see a small part of him but he is obviously waiting to enter the scene and attack. (00:14:00)
Day 3: 11:00 A.M.-12:00 P.M. - S3-E23
Revealing mistake: When Sherry is shot, the impact is visible on her shirt, but no gunshot wounds can be seen on her skin underneath, which can be seen as she falls to the ground.
Answer: According to Jack in season 5, Nina was "deep cover" before the pair ever met, so it's safe to assume she was recruited before she joined CTU. As for what her primary mission was, who knows? Perhaps it was to gather sensitive intel and pass it on to her superiors. Given that she worked for an intelligence agency, it's not a stretch. Or perhaps we may find out in season seven.
Cubs Fan ★