Character mistake: Just after Necros has infiltrated the MI5 safe house, captured General Pushkin and then escaped, M says that thanks to Necros, there are "2 dead, 2 in hospital." However, in fact Necros killed or seriously wounded 5 people, not four. First of all he kills the cook by strangling him. Then he gives the butler incredible burns on his face before knocking him out and leaving him with serious injuries. Then, as Necros walks out of the kitchen, two MI5 agents confront him with guns drawn. Necros throws a milk-bottle grenade right at their feet. This certainly either kills or seriously injures both men (a grenade at your feet is pretty devastating). Then, Necros throws another milk-bottle grenade at an MI5 agent standing on the staircase, which explodes, either killing or seriously wounding him. That is 5 agents, not 4, who Necros has seriously injured or killed, not including the milkman he also kills at the start of the scene (who may or may not be an MI5 agent).
Audio problem: Kara asks Bond in the plane cockpit what happened to the bad guy. He replies that he got the boot. His lips don't match what he says however.
Continuity mistake: When Bond lasers through the police car, the laser is at right angles. But, in close up shots, the angle is different.
Continuity mistake: When Q is demonstrating the stun gas/explosive key ring, when Q holds the keyring it's very slim. However, when it is placed on the desk and emits the stun gas, in close up it is very thick. This is obviously to make such a slim device emit the gas (probably an under the table gag).
Revealing mistake: Saunders is not in the door-way when the bomb launching the glass door goes off. He actually jumps forward to get there in time to get caught.
Continuity mistake: When Bond pushes Pushkin back on the bed in the hotel room, Pushkin has a basket with a bottle of champagne in his left hand. It disappears between shots, and there is no sound of it falling to the floor.