Revealing mistake: During the gun battle after Renard escapes the bunker, someone gets shot, and you see the stunt bloke dive to the floor and scream even though the gun wasn't even pointed at him or any bullets fired. He's the one standing just to the right of the jeep as we look at it.
Revealing mistake: During the ski chase, a paratrooper pulls out a submachine gun and fires a volley of bullets at Bond. However, as these hits the ground, you can see that actually there are two parallel lines of explosions behind Bond. The submachine gun can't possibly shoot two regular lines of bullets like that.
Revealing mistake: Right at the beginning of the boat chase when Bond drives the boat through the waterway in MI6, before he jumps the boat into the river, there is a shot roughly from Q's POV, the boat clearly slows right down before it reaches the end. It couldn't fly as far through the air as shown.
Revealing mistake: During the action sequence on the labyrinthine docks on the Caspian Sea, one of the choppers with the rotating blades saws Bond's BMW in half. A cutaway shot reveals Bond nearby, murmuring, "Q's not gonna like this." The next shot is in back of Bond, seeing the newly split BMW fall apart, but Pierce Brosnan has been replaced with a dummy. This is most obvious during the over-the shoulder shot of the BMW falling apart, where Bond's gun is now held in front of him. Also, when the car splits in two, the dummy shakes a bit.