Factual error: When Edgar proves that Mary-Ann Taylor framed Sarah to be the rat in CTU, he claims that she remotely took control of her computer by sending the signal over "a plain old AC power line." This is not possible, unless the computers were equipped with special hardware to separate the AC from the signal. If they were, this traffic would have been observed by James Heller's assistant.
Continuity mistake: When James phones Jack, who is at Tony's house with Audrey, Jack says they are at "21408, Kipling, North Hollywood". Later, when Secret Service arrives to pick up Audrey, Jack walks outside the house, where we see the house number is actually 21048. The same can be seen earlier when Tony, Audrey and Jack first arrive at the house, but not as close-up. (00:25:05 - 00:30:05)
Continuity mistake: When Curtis Manning is chasing Mary-Ann Taylor out of CTU, you see Mary-Ann exiting through a solid grey door marked by an EXIT sign in a wall which looks like concrete. As she passes through the door, you can see sunlight on her from almost directly above. In the next shot Mary-Ann is seen exiting through a glass door in a wall of glass panels. Unless there is a section of CTU's roof missing, the room she exits from in the second shot is not the room she exits to a few seconds earlier in the first shot.