Character mistake: Nicole Wallace has murdered and stolen the identity of Professor Elizabeth Hitchens, who was Australian. While speaking to Detective Goren she refers to her life in Melbourne, pronouncing it the American way : "Mel-born." No Australian would do such a thing - it is pronounced "Melbun." A detail-obsessed knowall like Goren would pick up on that immediately.
Character mistake: 23rd minute. Jack meets the female assassin in Anderson's apartment. She demands that he show his credentials. Jack says he's with CTU on a provisional basis and therefore he has no badge. The agent that came with Jack confirms that. Yet, in the 13th episode (minute 14) when he enters the sports shop with Audrey's husband, he shows his CTU badge to the owners in order to prove that he in fact is a federal agent.