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. (00:01:35)
Continuity mistake: During the yacht scene, Severine and Bond are standing looking out to the island. Severine is barefoot. Once on the island, she is wearing black heels. If she knew that she would need shoes to walk on the island, which is filled with rubble, she would already have them. She would have to walk back to her room on the yacht to get them. This is highly unlikely given the fact that they are being held hostage, and she could use her heels as a weapon.
Other mistake: When M is attacked by Silva during the parliamentary committee's hearing, Silva enters the room from M's back and M turns 180° around her own axis to face Silva - now M's own desk is at her back, that is, her very own desk cannot and is not protecting her from Silva. A few seconds later, after the gun battle intensifies, her desk is now located between herself and Silva, and she is using the desk as a protective shield against Silva's bullets. (01:40:45 - 01:41:20)