Factual error: The bad guys talks in German to Jack Bauer, posing as a German weapon dealer. But the German dialogue is very hard to understand, full of errors and with heavy accents - especially from Jack. After the first sentence his cover would be blown. (00:32:40 - 00:33:15)
Plot hole: Day 8: Renee mentions that after her previous sting operation with the FBI against Vladimir Laitanan, he had major facial reconstruction surgery, but in all of the photographs of said operation she shows CTU New York, Vladimir looks exactly the same as he does now.
Other mistake: In the car Jack practises his cover story posing as a German arms dealer. But when he mentions his fake name Ernst Meier he says it in the English way, not in the German one. No man with German language knowledge would say it in this very wrong way, and it would give him away immediately. (00:22:05)
Revealing mistake: When Farhad Hassan brings the press ID for Meredith Reed to security, you see the guard walk through the metal detector wearing his police belt, but the metal detector does not go off, showing that it's either not real, or not turned on.
Character mistake: When Chloe is talking to Arlo about the call Jack made to Meredith Reed, Chloe says that the call was made to Meredith's cell phone. But at Meredith's office, a coworker tells her the call is waiting (implying Jack called the office instead of Meredith directly), and once in her private office, she picks up the receiver of her land line. With all the phone tracing technology CTU has at its disposal, Chloe should be able to distinguish between the two.