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.
Plot hole: James Bond shouldn't have gotten away at the end of the airport scene where he steals an airplane and pretends to be a flying instructor. He had no wings with which to fly away and he ended back up right outside the airport, so the henchmen, who seemed to still be chasing him one shot before he parked, should have been right on him waiting when he got out of the plane.
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.
Continuity mistake: When Bond is on the small isle in the crocodile pond, one of the crocodiles begins to climb the rock. Cut to Bond and then back at the crocodile who has now turned into an alligator. In the next shot it is once again a crocodile.
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.