Revealing mistake: When Largo escapes to Disco Volante, he closes the underwater hatch before Bond arrives. But the hatch can't close completely. A hole is visible (and light from behind). The hatch is obviously created in a studio, because the boat would not be able to sail - at least not that fast - with such an opening in the bottom.
Continuity mistake: When the rear part/gunners' platform of the Disco Volante fights a delaying action, there are two speed-boats and a destroyer on the 'good' side. But although two close shots show the boats firing their on-board machine guns, only the platform and the battleship are visible in the same frame during the shoot-outs. There is no further indication that the speed-boats are destroyed or further involved in the eventual destruction of the platform.
Revealing mistake: At the end of the film in the underwater fight scene, when Bond is zooming through the water, you can see the cable pulling him along through the water.
Revealing mistake: Near the end of the film, when the bombs are on board the mini-sub, Bond is spotted by Largo and swims away, but is chased by one of the other divers who has a fight with Bond: Just before they get to grips with one another, you can see that the jacket of Bond's underwater suit is already torn at the right shoulder.
Continuity mistake: Just after Vargas has been harpooned and impaled to the tree, watch the position of Domino's hands as she says to Bond "I'm doing this for my brother for what he did to him" in between shots: When she has her back to the camera you cannot see her hands, but when you see Bond from behind, she has both of her hands on his shoulders.
Continuity mistake: When the woman in black locks the door and puts her coat on a chair, you can see her face through the veil, but as Bond rises from his chair, the veil has become much darker and we're unable to see the face behind it.
Answer: Look up Skyhook online and you'll find out how it was done. The person hanging from the cable wold be pulled aboard by the plane's crew.