Before Patrice enters the elevator in Shanghai, the button for his floor is already lit. After he motions to press the floor button, it is no longer lit. Later, as the elevator is moving up, the button is lit again.
When Bond rams his bike into the fence to get on the train where he fights Patrice, the bike can be seen flipping and lands on the track to the right of the moving train. In the second shot after, filmed from the opposite angle, the bike is not standing where it supposedly landed.
When Silva challenges Bond on Silva's island to shoot a glass off of Sévérine's head, one of Silva's henchmen points a gun to Bond's head. As camera angles changes, the position of the gun moves from shot to shot from being directly pressed against Bond's left temple, to a few inches away, to pointing more towards his cheek.
In the Shanghai Tower scene, the terrorist/sniper is seen operating a manual, bolt action rifle. Right after during the fight with James Bond, the gun is shot several times just as if it was a semi-automatic weapon.
When Bond is in M's flat, he puts down a bottle of Macallan whisky. When he is seen again, the bottle has been turned round, displaying the front label. In the next shot, the bottle is back to as it was.
When M is testifying to the ministers at parliamentary hearing, near the beginning of the scene, her wrist watch shows the time at 3:00. After about 5-10 minutes of dialogue, Silva approaching and Bond running down Whitehall, when they show M again reading poetry, her wrist watch shows the time at 3:55.
On the sailing yacht Bond puts the radio device in the right side pocket of his trousers, but when he shows it to Silva he must have taken it from the left pocket because his right hand is holding a gun.
When Severine is first seen on the deck of the yacht, she is standing forward of two rather large winches. James walks up and stands beside her. In the next shot after the conversation, they are both standing just aft of those winches.
In the first chase sequence before Patrice rides on top of the Grand Bazaar in Istanbul there is a sign beside the stairs that says "PANTOLON" with a piece of paper on the first "O". In the next two shots it was missing.
When bond is sitting on his own in the beach bar, he throws cash over the bar and takes a bottle of booze, pours himself a half glass then hears the report about the attack on MI6. In the next shot, the glass is empty though Bond doesn't touch the glass after he pours the drink.
When M is first debriefed by Gareth Mallory, she enters carrying a handbag, which she places on the floor beside her. The meeting ends abruptly and she leaves, and is not carrying her handbag, but she is not seen picking it up.
When in Shanghai, Bond is seen removing his gloves (particularly the right one) to use his gun. When hanging on to the lift he is seen without any gloves. Then when Patrice is hanging down from the building, 007 holds him with his right hand in the glove, which should be off (like in the previous shots)
The tube train used during the underground chase scene is a Jubliee line train as shown by the colour of the bars and the layout of the interior. The line the chase occurs on is the District line as proved by its final destination being Wimbledon.
During one of the beginning scenes, after Bond crashes his bike into a bridge wall and lands on top of a moving train, he almost slips off, but we see in a scene of the train moving away from the bridge that there is a platform which was supporting him as he was climbing back up onto the roof.
The opening chase scene is shot at two different provinces of Turkey, namely Adana and Istanbul, approximately 950 km apart. It is not possible to see yellow cabs with license plate numbers starting with '01' (signifying 'Adana') near the Grand Bazaar (in Istanbul).
The suggestion is that the building the Ministerial Hearing is being held in is in Westminster, in one of the Ministerial buildings off of Whitehall, however the building 'Silva' enters seems to be Trinity House on Trinity Square, close to Tower Hill and the Tower of London, several miles away, with Bond and others exiting the building after the shootout onto Seething Lane Garden.
Both Silva and Bond slide down the center escalator divider in the chase in the tube station. This would not be possible since, on the London Underground, there are protruding metal discs at regular intervals to prevent exactly this behavior.
In the intro scene when James Bond's train car is uncoupled, the car's brake pipe is disconnected as well. Train brakes work on positive pressure, so if the brake pipe were disconnected, the uncoupled cars would immediately stop within a short distance, and the rest of the train would shortly follow. In the movie, the uncoupled cars continue closely following the train as if nothing had happened.
When M is reading Bond's obituary, he is referred to as 'Commander James Bond C.M.G. R.N.'. A Royal Naval officer's rank is always either written in full ('Commander James Bond CMG Royal Navy') or fully abbreviated ('Cdr James Bond CMG RN').
After Bond and M arrive at Skyfall they review the available weapons with Kincade. Kincade hands Bond what looks like a double barrel shotgun and says that is was his father's hunting rifle. This is an "express rifle", a double barreled large caliber rifle designed for dangerous game at close range, and easily mistaken for a shotgun.
Bond's father's gun is manufactured by Anderson Wheeler, so it might seem unlikely that Andrew Bond, a representative of the arms manufacturer Vickers, would have habitually used a competitor's product. But given the fact that Vickers only built military weapons and never produced sporting arms, it is perfectly normal that he would have chosen a double rifle from one of the big sporting guns firms in Mayfair.
When the tube train falls through the hole into the area below, all its lights are still working. Once each carriage leaves the rails, which carry the electric current, these would all have gone out and the train would have been in darkness.
When James Bond chases Silva on the London Underground train, all the signage and stations suggests it's a District Line train; however this is actually 1996 Jubilee Line stock. This can be seen by both the colour scheme and deep level line body type.
The helicopters which arrive at Silva's lair on Hashima Island are not heard until they appear immediately overhead. These aircraft are extremely noisy, and can be noticeably loud even when a mile or two away.
After the terrorist attack on MI6, TV reporter explains that six people died and others were injured in the hospital. In the next scene, when M stands next to the coffins, we can count eight coffins that were the victims of the attack. However, the additional coffins could be explained that two of the injured had subsequently died of their injuries.