Audio problem: When Bond and Honey are on the beach the hoods of Dr No come by boat. On the boat there is a guy shouting through a megaphone. As they sail away again the man waves the megaphone to his comrades and says "Full Speed Ahead". Yet his voice sounds identical to when he was speaking through the megaphone, though he isn't holding it to his mouth anymore.
Continuity mistake: The hearse that was involved in Strangways death and later chases Bond is a 1937 or 1938 Lasalle,with the pod style headlights mounted on stalks on either side of the radiator. The car that drives off the cliff and explodes is a later model car, with the headlights mounted flush into the fenders.It is very easy to spot while the burning car is rolling down the side of the cliff.
Other mistake: After the decontamination chamber scene, Bond and Honey drink a cup of tea. Honey very quickly passes out due to the tea being laced with some type of sleep inducing drug. However, as Bond throws his cup in anger, Honey flinches very hard. Surprising considering how quickly she passed out after drinking the tea.
Audio problem: When the powerboat shoots at the island, afterward, when the guy with the speakerphone tells them that he would be back later on, he then turns to the driver and tells him to move on, but when he says that, it sounds as though he's still talking in the microphone even thought the microphone is at his side.
Plot hole: When Bond, Quarrel and Felix sail to Crab Key, Felix says that it's 48 hours to the moonshot. Bond replies that they'll "Be back in 12, if not then it's your beat and you'd better bring your marines with you". We know that Bond was still on the island when the rocket took off (it's when he kills Dr. No) and yet it's only when He and Honey are sailing AWAY from the island that Felix shows up with the marines. Why did he wait the full 48 hours (longer even as the moonshot had already occurred) when it was obvious something was wrong when Bond hadn't come back after the 12 or so hours as agreed?