Factual error: When Mrs. Logan escapes, Aaron Pierce refers to her as "the First Lady" over his radio. The Secret Service has code names for each of the members of the president's family. He should have used her code name when communicating to other Secret Service agents about her.
Continuity mistake: During Episode 3 of Season 5, the terrorists take Derek in front of live television. When the terrorists force him on his knees, you can see a splatter of blood on the floor from the body of the last victim that was shot there. As time is running out, another shot of Derek being held by the terrorists is shown, and the mere splatter of blood that had been near his knees is now a noticeably big pool of blood. Nobody has harmed Derek yet, and there are no signs that he is bleeding. So where did all that blood come from?
Continuity mistake: Season 5 - 9pm-10pm, at 9:41pm. - Technical weapon error. When Jack takes the Federal Marshal's' Glock pistol, in an effort to add drama, he holds the pistol in his right hand and cocks it with his left hand by grabbing the slide, pulling it back, and releasing it to chamber another round. However, after he does this, the camera zooms in on the gun as it is pointed at Colette's' head and you can see that the slide is still back on the gun and NOT capable of firing at all.
Audio problem: In the scene where the President Logan is in his office and planning to take his own life, he gets a phone call from CTU's Miles Papazian. When President Logan answers the intercom, his voice sounds like he is the one talking through the intercom, eventhough the camera stays on President Logan. After answering the intercom, his voice changes back to normal.
Plot hole: Martha Logan told Evelyn about the transcript and hid it in her bra in front of her. Yet when Mrs. Logan later tells her husband about it Evelyn doesn't seem to have any idea what she is talking about. While it can be considered a character choice for Evelyn not to speak up, there is no reason at all why Martha, who is so desperate for her husband to believe her, doesn't ask Evelyn to verify it.
Continuity mistake: Season five, 5th hour. Lynn knows about the four people who knew Jack was still alive, he mentions their names and talks to Jack about it. Yet when they are told Tony wants to speak with Jack, Lynn looks completely puzzled and Jack tells him that he knew Tony. Minutes earlier Lynn already knew that.
Continuity mistake: When Agent Aaron Pierce steps out of the helicopter, the right half of his face is severely wounded, with lots of blood and a bandage on it. 12 minutes later, when he is back in the Presidential house, he's talking with Miss. Logan and his face is completely clean, with not a single scratch or sign of wounds on his right half of the face. (00:12:55 - 00:25:00)