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.
Character mistake: At the airport, when Jack is under the bus on the trolley being towed by the truck, an accident causes all the cable on the winch reel to pay out. At this point all that's holding the cable to the reel is a small metal clamp. Jack slews around under the bus for a while, in grave danger of being run over by the vehicle's rear wheels, and then the clamp gives way (in slow motion). The now-free cable shoots toward the bus, and Jack pulls himself off the trolley just as it goes under the rear wheel. If you look at the shot where the cable is flying toward the bus, you can see two SWAT guys standing on the back of the truck, on either side of the winch. Their posture is completely relaxed and casual. Considering that for the past several seconds, Jack has been sliding around under the bus, fighting for his life, wouldn't the SWAT guys be much more excited--moving around, trying to get a better look, giving instructions to the truck's driver?