Continuity mistake: When Bond and Felix Leiter are underwater snooping around Lago's boat, Felix can be seen in diving gear minus a hat. After Bond gets sucked into the boat and Felix returns to land, you can see Felix take off the hat that was not in the previous scene. (01:30:30 - 01:32:50)
Continuity mistake: When the horsemen arrive to where Domino is tied up, the watcher has a cigarette in his lips, but it appears in his hand in the following shot. (01:44:25)
Revealing mistake: When Domino and Bond escape horseback riding, a man fires a rifle, but no smoke comes out despite the bang being heard. (01:47:07)
Continuity mistake: When Bond and Domino jump into the water from Palmyra with the horse, Bond is wearing a very tight fitting brown jacket and shoes. When he emerges from the water a second later, he is shirtless and shoeless. (01:48:15 - 01:48:55)
Factual error: The SEALS in the cave shooting use the out-dated M3 'Grease Gun' and the no longer produced MAC 10 for combat, while Largo's forces use Heckler&Koch MP5's. Actually, the SEALS should have MP5's as well; these weapons were and are standard issue of military and police special forces in the US. (02:01:30 - 02:03:45)
Continuity mistake: When Bond enters the tunnel, a workman at the entrance disappears in the opposite angle.
Revealing mistake: During the credits, Bond grabs a rope and jumps inside a house. His stunt is way younger than him and very noticeable.
Revealing mistake: When the movie begins Bond climbs up a telephone pole. From behind he is obviously not Sean Connery: not only his build is different, but his hair is a weird squared wig, maybe some sort of security helmet.
Continuity mistake: Bond throws a grenade at two guys playing chess. The deck of cards next to them disappears in the aerial angle but reappears in the close-up.
Visible crew/equipment: When Bond arrives at Shrublands the moving boom mic's pole is reflected on the car's windshield.
Revealing mistake: When Jack's car crashes, the actor with a military hat is replaced with a stunt driver wearing a silver helmet.
Revealing mistake: After Bond throws urine at the thug, and he collapses with all the glasses stuck to his back, note the protruding pad underneath his shirt where everything's been attached to.
Continuity mistake: The first time we see Blofeld he is touching the cat's head. A shot later his hand is on the cat's body.
Continuity mistake: The nurse asks Bond for a urine sample and tilts the beaker forward. A shot later it's tilted towards her.
Continuity mistake: During the credits, after Bond knocks out a guy in a terrace his hat is either close to his head or away depending on the shot.
Visible crew/equipment: At the star of the motorbike chase the camera man is in the motorbike wing mirror several times, and he's wearing a completely different type of helmet as well.
Revealing mistake: Small black ramps are against the kerb for the stunt rider to use to mount the pavement during the motorbike chase.
Revealing mistake: When Bond rescues Domino from being sold, and she hops on the horse, Kim Basinger is replaced by an obvious stunt.
Continuity mistake: Domino grabs the pendant with her hand positioned sideways. In the close-up, the palm of her hand is face up. Then it swaps to the previous position.
Continuity mistake: When Nigel falls in the water, his hairstyle changes between shots. Sure there's a two seconds shot in between, but that would mean that Nigel had that short lapse to let go his suitcase, bend his head backwards, comb his hair and grab onto his suitcase again... Impossible.
Chosen answer: Neither is a professional dancer. Having studied dancing some thirty years before does not mean someone has retained the same level of skills. As you mentioned, Connery was in his 50s by that time.
raywest