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.
Factual error: James Bond is seen running down Whitehall in London. Behind him a number 38 bus is seen. However the 38 does not travel down or indeed particularly near Whitehall. This was probably done to show off the new Routemaster bus, which is currently only used on the 38 route.
Factual error: When Bond is chasing Silva through the London Underground system they both supposedly get on a train at Temple Station on the District Line. The train is in fact a Jubilee Line train, but with District Line route maps on the inside. The back said Elephant & Castle and the front said Wimbledon.
Factual error: In the car scene just before the MI6 explosion, invalid IPv4 addresses (with digits larger than 255) are displayed on the laptop screen. [This gets debated, with comparisons made to 555 phone numbers. 555 may not be a real area code, but there's nothing technically preventing it being one. IP addresses, however, just can't have numbers larger than 255 - it's like a phone number having a % symbol in it.]
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: Bond and Silva travel from Temple station on the District/Circle line, which is a sub-surface line that has square tunnels (dug out from above and then covered over) and uses large trains with an almost square cross-section. However, the train they board is of the type used on the deep-level lines (eg. Northern and Jubilee lines), smaller and almost cylindrical in shape, and is seen to fit snugly into the cylindrical tube tunnel as the train leaves the station. They therefore can't be travelling on the District/Circle line, and must be on a deep-level line instead. The disused Jubilee line platforms at Charing Cross are often used for filming, and photographs available online show one such platform recently dressed as Temple station.
Factual error: When Bond drives M away in the Jaguar XJ, police cars can be seen driving towards them when he speeds around the corner. The Volvo police car in front has two yellow dots on the top of the windscreen which mean armed response, but on the roof there is a circle, which means traffic/incident response. The aerial roof marking symbol should have been a five-edged star for armed response. Metropolitan police don't even use Volvos for armed response. They use BMW 5 series and X5s.
Factual error: When there is a BBC News Report for the BBC News at 10 (clock bottom right) the wrong news studio is used rather than the correct one. They also used the wrong opening standing position. The studio shown is for the BBC News at 6pm, and the position used is only used for the intro after the half way segment, not the lead headline.
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.
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.