Continuity mistake: When Wai Lin handcuffs Bond to the water pipe (after the motorbike chase) she has a red shirt on over a white vest. When she turns to walk away the red shirt has disappeared.
Other mistake: When Carver is typing Bond's obituary on the big screen, he hits many more keys than would be necessary to write the end of the sentence.
Continuity mistake: In the scene where James is trying to escape from Carver's headquarters, a black guy holds him over the newspapers being printed. In one shot the back part of his tie (that hides behind the larger front part usually) is hanging by his ears, it cuts to a shot of the black guy and when it cuts back, the back part of the tie has risen back to its proper place against his chest.
Factual error: A Type 23 Duke Class Frigate is used as 'flagship' for the fleet at the end of the film. The Type 23 is way too small and undermanned to act in such a capacity; it has no command and control facilities. They should have used at least a Type 22 Batch 3 Frigate, a carrier or an LPD (Landing Ship). We also see the evidence of a fleet on their radar screen, but nothing more of them.
Plot hole: The helicopter bike jump was pointless as the helicopter was low down looking for them, not knowing they were in the building - Bond could have turned the bike around and gone back the way they came.
Revealing mistake: When Bond drives the BMW at himself and Q in the hangar, it cuts to an interior view of the car. This scene has obviously been sped up to give the impression that the car is going faster than it actually is, evident by the vehicle's speedometer.
Continuity mistake: In the car park, when Bond activates the car-camera the phone screen shows the car next to Bond and the black and yellow column, but not Bond, despite him being in sight.
Continuity mistake: When Bond finishes testing the remote car he and Q stand close together in the front angles. In the wide angle from behind they stand half a meter away from each other. This swaps back and forth.
Continuity mistake: When Bond is about to fire at the car park metal door there's no-one next to it. A shot later two guards can be seen in front of the door, running away.
Continuity mistake: Before the remote BMW comes to a stop Q's hands are on his back. A shot later they are by his side.
Revealing mistake: The first time Bond uses the remote car, there's a bulky black object moving on the rear seat, obviously a hidden driver.
Continuity mistake: When Bond and Wai dive into the fountain to hide from the helicopter, clothes and pots appear/disappear randomly between shots.
Revealing mistake: In Saigon, when Bond pops a wheelie skid marks from previous takes can be seen on the road.
Continuity mistake: At the car park, Bond disappears in all the wide shots of the car but reappears in the close-ups. This was due because the stunt driver was seated in the back seat.
Continuity mistake: The scene where Carver is writing the newspaper headline, he changes it from "British sailors killed" to "British sailors murdered." The camera then cuts to a close up of his face, and reflected in his glasses we see the other page (with the headline in different languages). The top text box changes so it has two rows of text. However, when the camera cuts back as Stamper calls in, there is mysteriously only one line of text again.
Factual error: Carver successfully frames the Chinese airforce for sinking the HMS Devonshire, making everyone believe that they torpedoed the ship. The problem with this is that the Nanchang Q-5 can't carry torpedos.
Character mistake: Both the stealth boat captain and the British captain of the HMS Devonshire refer to the Chinese aircraft flying overhead as MiGs. However, the aircraft are in fact Nanchang Q-5s.
Revealing mistake: After Bond's BMW runs across the spikes that deflate the tyres, there follows a side shot of one of the rear tyres re-inflating. If you look carefully, under the car near the wheel is the mechanism they used to raise the car to 're-inflate' the tyre.
Factual error: In the Oxford scene, Bond is in bed with the Danish professor in the New Buildings wing of New College. The problem is that all the rooms in the New Buildings are student rooms and have always been so since they were built - no professors live or teach in this building. The professors are on the other side of college.
Factual error: In the first minutes of the movie, Bond is in an Albatross L-39 ZA, ejecting his enemy (in the back seat, who wants to strangulate him), not himself (in the front seat). Bond unlocks the ejection system with the switch on the console, but in reality ejection in that aircraft is triggered by a double firing handle on the seat pan.
Answer: Elliot Carver arranged it, he called Dr. Kaufman, who said, he is a specialist in arranging the perfect murder. His specialty is the celebrity suicide.