Continuity mistake: After Bond gets picked up from the airport, evades a car, then fights with the driver, at one point he pulls back his right arm, but then the angle changes, and he hits him with his left one.
Revealing mistake: When James Bond has a spider on his arm, one can see he's under a glass plate, and the spider on top of the plate.
Factual error: When Bond is involved in a high-speed chase on the way to Miss Taro's house, his wheels are squealing like crazy, but he's on a dirt road.
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: Bond sits down by a table, puts some cards down, and pulls his gun out. He's wearing a tie, but when we see a closeup of him screwing on the silencer, his tie disappears.
Continuity mistake: During the car chase on the way to Miss Taro's house, we can see the same shot of the cars at the turn three times.
Continuity mistake: When Bond enters the office of Universal Imports he throws his hat on the hat rack. After his meeting with M, he retrieves his hat from the hat rack, but it has moved to a different hook.