Renard's file states that the bullet is traveling through his 'Medulla Oblongata'. This is actually the part of the brain at the lower part of the brain stem (therefore towards the back and the furthest point down of the brain). When we see the 3D image of Renard's head and brain we can see that the bullet is actually traveling through the left side, at the front of the brain within the top portion of the brain, this section is actually the Frontal Lobe (or Cerebral Hemisphere)and nowhere near the Medulla Oblongata.
As Bond jumps through the door in the underground shootout, we see a brief shot of him bounding headfirst through a door, with his gun outstretched. Closer inspection reveals that the gun was discharging during this jump, but no sound is heard.
It is stated that the bomb traveling in the pipeline is traveling at 70 miles per hour and has to cover a distance of 106 miles. Bond states that this will take 78 minutes. To cover 106 miles at 70 miles per hour would actually take 91 minutes. However, Bond admits in GoldenEye that he was never good with numbers.
Elektra King claims to be of Azeri descent on her maternal side. Thus she thinks she is saving her cultural heritage by rerouting the pipeline around the church. But the church as proved by the priest is Russian orthodox and that is far removed from Azeri culture.
After Bond enters the submarine, he threatens a crewman by holding an M1911 type pistol with the hammer down at the crewman's head. The gun cannot fire in this aspect and it does not make sense that Bond would enter a hostile submarine so disarmed.
During the caviar factory battle, Bond hides behind a table, holding his P99 pistol as he yells, "Get out!" to Valentin and Christmas. After a cutaway, Bond is holding a machine gun, then after another, he fires the original pistol.
During the opening scene, before Bond jumps out the window, he is clearly shown tying the curtain rope to his belt (this is also seen again as he is falling). Yet, when he lands on the ground, he simply lets go of the rope and walks off without undoing it.
In the Millennium Dome chase sequence, just before Bond jumps from Q's fishing boat to the balloon, the canopy on the boat is present. When Bond actually makes the jump, the canopy has disappeared without explanation.
In one shot during the caviar building action sequence, Bond opens a hatch and climbs out onto the dock, with an empty gun (the slide on his pistol is locked back), and yet he fires it above him, shooting out the feet of the man above him.
Just before the Russian submarine surfaces below the tower in Istanbul, a wide shot shows the ship it used for cover going by the tower, built on a very small island, considerably smaller than the ship. In the next shot the submarine is surfacing in a hall which is at least twice as long as the whole island.
During the caviar factory scene, you see the helicopter hovering above Bond's BMW. The helicopter has the blades suspended beneath it, but when Bond destroys the helicopter, the blades are no longer there.
When Jones is waiting for the indicator to turn red, the button cover is closed. However, when she goes to press the button the cover is open but she gets pushed away. When she again goes to press the button, the cover is closed again.
In the underground base, when Bond is rushing to get to the door, it is almost completely shut. In the next shot, when Bond is diving through the door, it is only about half shut, giving him enough time to jump through it before it closes.
At the end of the boat chase, when the Cigar Girl blows up the balloon, you see Bond rolling down the building; all his hair is wild and uncombed. When he grabs the wire and stops, his hair is nicely combed down and a few hairs in front are a little wild.
At the end of the boat chase, when Cigar Girl's Sunseeker boat hits the shore below the Dome, it is clearly low tide. The boat beaches quite a way short of the river wall. Seconds later when Bond's boat jumps over the Sunseeker, it is clearly high tide and the Sunseeker's bow is now touching the river wall.
When Bond and Renard first come face-to-face at the silo, Bond puts his pistol on Renard's temple. When the camera cuts on Renard's line, "I did spare your life at the banker's office," the gun has changed position to Renard's forehead.
When Bond skis over the top of the para-hawk, and "slices" the parachute open, this scene is filled with errors. First of all, in the initial shot, his trajectory is way off, and he completely misses the parachute. Second of all, it cuts to a shot where the ski slices the parachute open, and the hole it makes is a long, wide hole. When it cuts to the next shot, there is only a very small, round hole in the chute, and the edge of the parachute is also frayed, despite Bond having done nothing to the edge of the parachute.
In the Swiss banker's office at the beginning, Bond is handed a receipt. From Bond's POV it is an A4 sheet but has shrunk to A5 when it cuts back to Bond as he starts to fold it. Later in the MI6 castle in Scotland he brings the receipt out of his pocket and it is once again A4.
Just before the parahawks give chase the camera looks down at the snow where Bond stands and there is no mark from his ski as if he was lowered to that location by helicopter before filming was started.
During the opening boat chase, the route actually taken through London's Isle of Dogs does not match the route displayed on Bond's on-board computer map. Specifically: The map shows the route through West India Docks, but the chase is obviously through Millwall Inner and Outer Docks. Further, the boats come out of what is, in reality, a dead end.
In the opening scene in Bilbao, Spain, after the shots, police sirens are heard, and several cars of the Spanish national police are seen through the window, at several different times. When the police enter the office, however, the uniform worn by the agents is not the one from the Spanish national police, but from the Basque police force, which would not have jurisdiction over this type of event.
Renard's file says that the bullet traveling through his brain is in the medulla oblongata, thus killing his senses. This area of the brain controls basic functions such as breathing and heart rate, not the sensory perceptions.
Even if the villains would cause the submarine reactor to overheat and be destroyed by a meltdown, this would produce rather small amounts of contamination, especially since it takes place under water. Istanbul would not at all need to be evacuated, which foils the entire plan.
It is extremely difficult to move a limb that is devoid of feeling, and a man who has no sensation anywhere in his body would need to learn how to move all over again; he would likely move very stiffly and awkwardly, and we don't see that.
The depiction of the submarine's nuclear propulsion facilities is complete fantasy. The notion that a submarine would have a smelting facility for shaping fuel rods is nonsense; refueling operations happen at port, less than a handful of times during the lifetime of the sub, not ad hoc underway. And where would they get the raw material for smelting? Also, a Victor III submarine has a VM-4P pressurized water reactor which cannot be opened and remain operating as shown as this lets out the water in the reactor vessel which is essential for it to function; the nuclear reaction stops when no water is present. Any operation such as depicted would scald, burn and heavily irradiate anyone trying, guaranteeing their immediate death.
Bond submerges Q's 'fishing boat' in the opening chase scene in order to pass underneath a closed drawbridge. However, there is no windscreen on the boat; submerging the boat at that speed would cause tear the roof off completely, or cause the driver's compartment to act as a huge water scoop and create massive drag.
At the beginning of the film, when Bond is in Swiss bank (in Spain), while reviewing the statement of account, the account listed is for "Sir Robert King", but the banker addresses him as Mr. Bond when the document is handed to him. Bond must be authorized to collect the money. The banker tells him "No doubt, Sir Robert will be pleased to see it again", showing that he knows Bond is not Sir Robert King.
When Bond drives his speedboat through the market during the boat chase scene, a view from the driver's perspective shows food and debris striking what is apparently a windshield. While his boat has no windshield, the police car following (whose perspective we see) does.
Assuming - wrongly - that a rod of weapons grade plutonium probably can cause a meltdown in a reactor, while it wouldn't technically be an "explosion" it would still be a massive release of energy. So that's a fair enough word, especially when used a non-expert such as Bond.
When Bond stands up behind the glass doors after the MI6 explosion, he is dry. When he climbs into the jet boat, he is already wet. This is from the sprinkler system that activated immediately after the explosion.
In the MI6 opening sequence we see a hole blown in the face of the building when the money explodes. When Bond launches the jet boat, the hole is gone. The hole is obscured by a lamp pole and the smoke from the explosion.
When Bond slices the parachute with his skis, not only is the damage in the wrong place and the wrong size in the next cut, but there is no reason for the engine to be sputtering once the parachute is damaged - it was not hit.
When Bond and Elektra are trapped inside the inflatable shield, it is dark. Bond turns on the lights on his wristwatch, and the entire place lights up. Bond moves around around a lot, but the lighting does not change at all, revealing that the lighting is coming from a different source.
When Renard holds the scalding rock, it burns his skin to the point where smoke comes out. After he lets go of the rock, there is not a mark on his hand. Despite the fact that he cannot "feel pain" his hand would still be visibly burned very badly.
After the gun barrel sequence, Bond walks down a street in Bilbao and you can see an old lady hiding and looking at him as well as the fans (some flashing cameras) being held back by a steel fence so that they don't walk in the scene.
In the pre-credits boat chase, just before Cigar Girl's Sunseeker crashes outside the Millennium Dome, the first-person view from the boat reveals that the broken railings on the wall which are seemingly caused by the boat's nose, are in fact broken prior to impact.
The helicopter supposedly cannot land because of severe wind. When James and Elektra disembark on their skis, the only wind action seen is that caused by the helicopter's own rotor, and the pilot manages to keep the helicopter still while hovering.
When the Helicopter with the saw blades is cutting through the BMW, the amount of sparks would have set off the gas tanks blowing the car up. Even if it didn't, after the car was cut in half there was no fluids of any type dripping from the car. No gas, oil, anti-freeze, etc.
The goof items below may give away important plot points.
When Elektra has Bond in the torture device, she takes off her right earring, showing Bond her injured ear. However, in the next scene where she steps behind the torture device the earring is back on her ear.
Bond was wearing a white shirt (and a suit) before killing Elektra. Right after killing her, he rushes to the underground dock for submarine and jumps into the water. Next he is shown wearing a blue shirt in which he gets into the submarine.
Near the end of the movie just before 007 boards the submarine, Elektra is handed the walkie talkie at gunpoint and ordered to call off Renard. When 007 says this, the camera, while facing him, shows him with his gun raised however when the screen shifts to Elektra, only his arm with the walkie talkie in hand is shown raised.
After M asks Elektra, "What's the time?", Elektra's body guard Gabor is seen to close the door to M's cell at Maiden's Tower. However, about a minute later, Gabor is all the way across the harbor in Istanbul where he and Elektra's henchmen take Bond and Dr. Jones captive.
At the end of the submarine scene, Bond and Jones escape from the rearward torpedo tube right before the explosion splits the sub in two. Yet when they are on the surface and waving to the tourist boat, the ocean is dead calm. With all the air escaping from the sub below them, the surface should look like it is boiling, and would draw serious attention from a passing boat.