Character mistake: There is no way on earth that a police officer would shoot a hostage in the thigh to 'take them out of the equation'. Anyone who suggested such a thing would likely be taken out and shot themselves. Bullet wounds to the thigh are often fatal, as an injury to the femoral artery causes massive and frequently unstoppable blood loss. Breaking the femur often leads to fat embolisms as bone marrow gets into the bloodstream and then to the lungs. In fact a broken femur is a life threatening injury in itself, and a shattered femur - a typical bullet injury - would almost always result in a total amputation. You cannot aim carefully enough to avoid the bone or artery as their position in the body varies, (as will the bullet trajectory upon impact). Jack is an experienced cop and would know the potentially disastrous consequences of shooting someone in the thigh. He'd shoot him in the foot. (00:21:05)
Character mistake: In the scene at Roger Podacter's condo building, you hear the reporter mention that he allegedly leaped to his death from his own 20th story balcony. As the camera pans down, you can see the flashlights and people up on his balcony doing the investigation. This is the 2nd from the top floor. If you count the floors as the camera moves down, there are more than 20 floors to this building. The number is actually closer to 30. Even though it is difficult to get an exact count of the floors, it is still possible to tell with 100% certainty that his unit was on a floor higher than 20.
Character mistake: When Guile promises to rescue the hostages while on camera with Bison, he makes it a point to mention Charlie by name to reassure him that he wasn't forgotten. Anyone in charge of a major hostage recovery operation would avoid naming a specific hostage unknown to the enemy due to the special focus that the enemy may put on that hostage for further abuse. This was promptly proven when Bison specifically chose Charlie to transform into a beast due to Guile identifying him as a personal friend.
Character mistake: A character mentions carbon-dating one of the fossils found. This is preposterous... you can't carbon-date fossils like the ones being shown. Radiometric dating maybe... But certainly not carbon dating. He's a professional and should know more than better that carbon dating wouldn't work.
Character mistake: Shiwan Khan uses mind control to make Nelson commit suicide. Later, when Lamont is talking to one of his agents, the agent talks about a murder at the museum.