Revealing mistake: The Union Flag pinned to the back of the taxi driver's jacket is upside down. Since he is part of the government (he's undercover for the Foreign Office) he shouldn't make such an terrible mistake. (01:20:40)
Continuity mistake: After drinking the drugged champagne Tremble collapses the instant he enters the bathroom. But when we see him passed out against the bath he doesn't have his braces and holster on. They're hanging over the side of the bath but there was no time for him to have taken them off. (01:26:30)
Continuity mistake: Each time Tremble does his 'Indian beggar' lines, there is a woman in a red dress standing right behind him. She is not there in any other shot. (01:35:35 - 01:37:30)
Continuity mistake: Tremble's chips are next to his glass of champagne. However, when we see a close-up of his first hand (3 of clubs and 3 of hearts), Tremble puts his cards down next to his glass, and the chips are not there. (01:37:10)
Continuity mistake: When Andress is taken hostage outside the casino, watch the background to see the bouncer walk inside the Royale. Yet, when Sellers runs outside, the bouncer is outside again. (01:41:00)
Revealing mistake: Mata is kidnapped and taken to Casino Royale in a flying saucer, which then releases a small hovercraft to bring her inside the island cave. Once inside the cave, the hovercraft leaves the water and goes up a ramp, at which point a tow cable can be seen pulling the hovercraft up the ramp and onto the landing platform. (01:45:25)
Continuity mistake: There are several differences between the miniature model of the hovercraft-like thing that Mata is in and the full-size model. For example, the full-size model has red markings near the antennae and a silver bottom, whereas the miniature has no markings and a predominantly red bottom. (01:49:35)
Continuity mistake: There is a hat on top of Jimmy Bond's piano. The strings hanging from it change position between shots. (01:56:15)
Continuity mistake: The cupboard in Jimmy Bond's torture chamber contains, among other things, a bowler hat. But when Jimmy opens it, to get his atomic pill, the hat is no longer there. (01:57:05)
Continuity mistake: When Jimmy Bond opens the cupboard to get his pills there is a mounted gun on the shelf as well. After picking up the pills he turns around and the gun has vanished. (01:57:15)
Continuity mistake: Early on in the fight at the casino someone smashes through the mirror above the bar. Later on the mirror can be seen to be intact. (02:05:25)
Factual error: When M and his entourage arrive at Bond's estate, their cars are surrounded by sheep. They then drive on down an unsurfaced road to Bond's house, past a pride of lions he keeps on the grounds. A series of sweeping overhead shots shows us that it is all one huge field, with no fences or the like. Those sheep aren't going to last very long.
Continuity mistake: When Miss Goodthighs comes in with a champagne bottle Tremble shoots and she says 'missed Mr Bond'. At this moment Tremble has no glasses. A few seconds later he says 'raise your arm' and then shoots at the bottle. He is now wearing glasses.
Visible crew/equipment: When James is visited in his chambers in the Scottish Castle by the "widow", someone is in the mirror as she enters. When she moves forward, and the film cuts back to her from James, the person is no longer in the mirror, even though the angle is the same.
Continuity mistake: When Bond, Moneypenny, his daughter, and his double are escaping from their prison cell, Moneypenny and Mata Bond are barefoot. When they are outside the cell, they both have their heels. They are never shown putting their shoes back on, and they wouldn't have had enough time anyway.
Continuity mistake: When Sir James and Mata Bond infiltrate Dr. Noah's headquarters, they hurry down a corridor with dozens of doorways. There are no flashing lights, but the corridor color repeatedly changes from blue with blue doors to red with red doors from one camera shot to the next.
Suggested correction: And exactly how would this have happened unintentionally? This was obviously done on purpose to create a disorienting, surreal effect. It may not be "realistic" but this is not a movie that concerned with realism.
Your attempt to speculatively explain it away as a stylistic choice does not negate the fact that this is a continuity error in a film that is full of continuity errors. It's important to remember that this film had 6 different directors, as well as disgruntled and uncooperative actors (Peter Sellers even quit and walked out in the middle of production). As a result, the movie has a piece-meal appearance and is riddled with plot holes and continuity errors.
Are you suggesting the two parts of the scene was directed by two different directors and one of them decided to change the color scheme before shooting? Considering the difficulty in creating the two different looks, it is practically impossible for this to have been done accidentally. A break in continuity is not a mistake if it is intentional.
Early in the sequence, Sir James and Mata Bond are looking for an escape route: They glance down one corridor, which is a dead-end that is all blue with blue doors; but they choose another dead-end corridor that is all red with red doors. As they flee down the red corridor, the camera cuts to show them from the front, back and profile as they hurry down the corridor. Although they deliberately chose the red corridor, the color changes from red to blue and back to red from cut to cut. The obvious answer is that they tried alternate takes Sir James and Mata Bond fleeing down the red corridor and then the blue corridor, but then sloppily edited the shots together into one sequence.