Factual error: During Bond's fight with Patrice in the Shanghai high-rise, Patrice's sniper rifle fires several times, presumably by accident. However, moments earlier, when Patrice assassinates his target in the neighboring building, the rifle is shown to be bolt-action. A bolt-action rifle can't be fired more than once without manually re-cocking the gun in order to fire the next round.
Continuity mistake: In a hotel room at the start, Bond finds Ronson bleeding. Note the amount of blood on his chin coming from his mouth. In the shot where Bond opens Ronsons's jacket partway to see the blood, there are a bit of dripping blood going down his chin. In the shot where Bond leaves the room, there is suddenly a huge blob of blood on the left side of the Ronson's lips that wasn't there before.
Visible crew/equipment: After Patrice jumps onto the train, Bond drives off the bridge and lands on the train and begins to fall over the side, then climbs back on. Eve then says "They're on the train." During this shot, you can see the white platform Bond was standing on to climb back onto the train.
Factual error: In Turkey the first two numbers of a vehicle licence plate belong to a city. Number 34, for example, is for Istanbul. The motorcycle chase in the beginning of the movie takes part in Istanbul (both the Land Rover and the Audi have "34" plates). However, once they come to the bridge where Bond jumps to the train, all the vehicles on the bridge (except the Land Rover) have plates starting with "01", which is the licence plate number for the city of Adana, where those scenes were shot.
Factual error: On the District line, Temple and Embankment stations do not have two platforms between each train. They actually run side by side, and not with the platforms in between the two trains.
Factual error: It would be impossible to drive a silver Aston Martin DB5 from London to Scotland without getting splash marks on the side of the vehicle. Especially in view of the fact that the road conditions are wet by the time 007 and M reach the Scottish Highlands, but the car still looks immaculate.
Factual error: When Bond climbs up from under lift/elevator after hanging under the assassin's lift car he opens adjacent lift/elevator landing doors just by pulling them apart. This is not possible without first disengaging the door lock mechanism, which is operated when car is at that level. If this were possible anyone could push lift/elevator doors open from any level and fall down the shaft.
Continuity mistake: Just after Bond has lost track of Silva in the London Underground station, the scene cuts to M's parliament meeting. At this time, the time on M's watch reads 3:00. Yet when Bond catches up with Silva in the basement of the London Underground station, the time on Bond's watch reads 4:55. Far too long to have passed given the events seen and distances travelled.
Other mistake: In the opening scene where Moneypenny is holding the rifle, you can see the flash suppressor was installed upside down. The 'slots' are on the bottom.