Continuity mistake: When the guy with the snake is shot Baron Samedi re-appears and you can distinctly see the bloke holding the snake again.
Deliberate mistake: In the scene where Bond and Kananga are fighting underwater, Bond shoves the bullet in Kananga's mouth. Then Kananga rises up and explodes. He explodes like a balloon, with not much blood at all.
Visible crew/equipment: Four patrol cars are chasing Bond and the villain by the road. Bond and the villain arrive at a dead end and they jump over the road with their boats. The four vehicles collide just after. Look carefully and you will see that the right-seat passenger of the red car and the driver of the blue one wear a yellow protective helmet.
Continuity mistake: When TeeHee is destroying Bond's gun with his mechanical arm, you can see that the gun already has a crease on it even before it is bent.
Factual error: In the scene where Kananga's henchman Adam is being interrogated by Sheriff Pepper by his car at the riverside, the boat chase arrives and two boats jump clearly over head disillusioning Sheriff Pepper and allowing Adam to make a quick getaway. However, as Adam is getting away in his car, screeches can be heard coming from the tyres, but they are on a dry dirt road.
Visible crew/equipment: When Bond and Solitaire are tied to the orange thing you can see a wire on the bullet which makes it fly across the room.
Revealing mistake: When Madeline Smith (The Italian agent credited as Beautiful Girl) emerges from the wardrobe / closet, she embraces Roger Moore. He then uses his magnetic Rolex to pull down the zipper on the back of her dress. If you look closely, you can see the cable/wire under dress pulling the zipper down.
Other mistake: When James kills the snake in his bathroom with the flame from his cigar and the aerosol, the carpet doesn't appear even singed.