Visible crew/equipment: When Mimi is escaping from the castle and swinging on the drain pipes, the wire holding the whole lot up is visible. (00:29:10)
Continuity mistake: While going quickly around a sharp bend, the milk float sheds most of its load. In the next shot, the back is full of milk crates again. (00:35:35)
Visible crew/equipment: After Mimi has cut off the magnetic button and launched it away with James' braces, there is a shot of the exploding grouse, and the wires making it fly are visible. (00:31:00)
Visible crew/equipment: In the shot where the 'Dual Carriageway' sign is seen and the cars drive over the camera, the man driving the milk-float that is meant to be being controlled by radio is visible. (00:35:25)
Continuity mistake: There is a scene where Ursula Andress spins in slow motion on her bed, while pink feathers float around her. In the next scene, you can see the pink feathers still in her hair. In the next, they are pink hearts. (00:52:50)
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: During the saloon fight, when a cowboy blows his trumpet, the hole that the arrow later passes through is already visible.
Revealing mistake: When the strongman grabs the boulder, falls backwards, and it breaks through the floor tile, a clear rectangular pre-cut in the floor is visible - made to facilitate the stunt.
Visible crew/equipment: Before Bond and Vesper walk through the secret door, nothing is cast in front of it. However, once the door closes behind them, a shadow - presumably that of the cameraman - is cast on it.
Revealing mistake: During the casino fight, when Bond kicks a man, he is suddenly replaced by an obvious stunt double with much thicker hair.
Visible crew/equipment: When the truck crashes, a filming camera is visible on the left side of the frame.
Visible crew/equipment: When Le Chiffre levitates the woman, after he conceals her hand, the metal rig used to lift her becomes visible in the top right corner of the screen.
Continuity mistake: When Vesper is lying on the bed taking pictures, her light pink robe suddenly appears dark pink in the very next shot.
Visible crew/equipment: When Bond reveals the coffin containing the toupee, the stage lights are reflected on the glass dome to the left.
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)
Revealing mistake: When the crowd watches the UFO, the group of people on the right can be seen through the now translucent tramp.
Revealing mistake: When the UFO releases the hovercraft, vertical creases are visible on the blue-sky backdrop behind it.
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)
Visible crew/equipment: When Mimi slides down the pipe, her safety cable is visible. (00:29:29)
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.
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