Many times in the series, the next episode starts at a point where not enough time has passed for something to have happened. For example, when Kim and her boyfriend are arrested by one cop and are have to lie down on the ground with their hands behind their head and then we see the clock beep for the usual 3 seconds into the next hour. Then the next episode begins, with several cops arrived at the scene, Kim being questioned by officers, sitting down, wearing a blanket. All of this could have not have happened in just 3 seconds. This happens several times throughout the series.
In many episodes in season one, you can see cameras on stands and men walking carrying them, such as when Nina is in the abandoned building in the construction site. Or when Jack is walking through the basement of the building where Senator Palmer is holding his breakfast meeting.
Many times Jack and others are seen stealing a car by quickly reaching under the dashboard to yank down some wires and intermittently sparking them together to make the engine start. This is impossible on many levels. Beginning in the mid nineties with the introduction of 2nd generation on board diagnostics (OBD II) all cars have theft protection that requires electronic input from the key or the computer will either shut down the fuel injection or not allow the starter motor to engage. Only a manufacturer's program (or a black market version) through the scan tool connector could bypass this. On an older car you would still have to remove the panel below the steering column (several screws) and even then the wires from the key lock and other controls are tightly molded together in bundles requiring a razor knife to separate and strip them. You would then have to connect constant power to the ignition (distributor or coil pack) and then hold the wire to the starter motor together with power for the entire time the engine needs to crank to start until releasing it, not just arcing it a couple of times.
Over the course of the series, several characters have speed dialed CTU on phones that did not originally belong to CTU or any other govt agency. Many times, they press a single button on the phone and the speed dialing sound effect is played.
In Season 1 Episode 4, time indicates 03:29 at approximately 17 minutes into the episode, and time indicates 03:30 at approximately 22 minutes into the episode. The show is on a real time schedule, so the time should correspond to each other.
In Season 2 Episode 2, it is shown that Michelle Dessler was on the helicopter with Jack Bauer at 05:42 minutes into the episode, but it is shown later that Michelle Dessler is at CTU headquarters at around 08:30 into the episode when George Mason got off the phone with Jack who just landed the helicopter 2 minutes ago. It is not possible for Michelle Dessler to get back from the helicopter in time in any ways if the show runs on a real time schedule.