Deliberate mistake: In the scene where the bad guy is attached to the missile and fired, in the split second before it hits the helicopter you can see below it a building called SUN BANK, but the letters are backwards. A close look reveals the likely reason - to the right of the reversed building is one which looks just like the building to the LEFT of the Sun Bank building behind the harrier a few seconds earlier. Most likely they couldn't film the chopper from the right side because there was a building there (the one the camera flies through), so they filmed it from the other side (the same side they'd filmed the harrier from), catching the "Sun Bank" behind, then had to flip it to have everything facing the right way.
Revealing mistake: During the scene where Arnold's character is escaping from the mansion at the beginning of the movie, there is a part where he is running down a snowy hill through trees. At one point during the hill scene, Arnold does a flip head first. When he lands the flip, you can clearly see the stunt double's face as he turns to shoot at more bad guys.
Revealing mistake: After the bathroom shootout, when Harry Tasker has his team contain the terrorist leader in front of the building they're about to chase through, just before the terrorist rides the motorcycle through the front door, if you watch carefully, you can very clearly spot Arnold Schwarzenegger's double on the horse.
Revealing mistake: During the shoot-out in the restroom, the villain fires shots down the length of stalls. Then as he walks down kicking each door open there is a shot from inside one of the stalls. You can see where the explosives were taped to the back of the door to make the gun shoot holes. There is residue on the back of the door and all of these rectangular clean area where the holes ended up being.
Revealing mistake: In the restroom fight scene, the first villain shot by Arnold randomly shoots his gun as he is dying. Some of the stray bullets hit the urinals. As the camera angle changes to show the bullets hitting the urinal, large flames can be seen as the urinal explodes and falls to pieces. There must have been a small explosive used to make this happen, as the bullet impact wouldn't do this.