Continuity mistake: Bond and Silva are in a train with a number beginning in 96 and ending in 69 (96269, 96469 etc) However, near the end of this scene, the carriages have now become 96424 and 96224.
Continuity mistake: When Silva gets out of the helicopter at Skyfall, the sky is approaching dark (7 o'clock to 8 o'clock sky). After throwing the grenades in the house and Silva says "Everyone listen to me! Don't you dare touch her, she's mine!" about 50 seconds later, it is suddenly pitch black (11 o'clock to midnight sky).
Continuity mistake: When Bond runs out of the London Underground Station, he is covered in dust. The dust is still there when he runs into the Houses of Parliament and still there when he drives off with M. Yet the dust has disappeared when Bond and M find the Aston Martin. There was no time to clean up the dust since he was driving.
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.
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.