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.
Continuity mistake: When Howard Payne is in the elevator, he hears Jack and Harry doing something from above, and he reaches for his bomb trigger. In slow motion when he's picking it up, it has two buttons on it, yet when Howard pushes one of the buttons, the device now has three. (00:13:00)The-Immortal