Continuity mistake: Most of the time that Le Chiffre is playing cards the women gathered around him are in the same position - e.g. the blonde twins are either side of him and the woman in the bright green dress is to his right. However there is one short shot, just before Le Chiffre does his levitating woman magic trick, where they are all in different positions - e.g. the woman in the green dress is now behind him to his left. (01:12:10)
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)
Revealing mistake: When the UFO lands and the ramp is deployed on the road, the last part briefly turns transparent. Additionally, a man walking past a red car fades and disappears as he approaches the ramp - a clear result of the composite image effect. (01:47:52)
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)
Visible crew/equipment: When Bond is arrested by a group of men, one of them carries a silver shield on his back, which reflects the set lights. (01:50:45)
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.
Continuity mistake: When the Secret Service car comes across the lions on the road, both their number and positions shift between shots.
Continuity mistake: Before being killed, when Evelyn is surrounded by bagpipers, his hair appears messy - yet in the following shot, it's suddenly neat and brushed.
Revealing mistake: During the saloon fight, when a cowboy blows his trumpet, the hole that the arrow later passes through is already visible.
Answer: Given that this is a comedy, the thinking was probably "Well, we'll just blow up your retirement so you've got no choice but to come out of it."
Captain Defenestrator