Revealing mistake: When Bond is driving down the dirt road, it's very obvious that the driver is Sean Connery's stuntman.
Continuity mistake: Bond grabs the golf club that Trench is holding and retrieves it towards him. A split second later, from the opposite angle, his hand is away and she's still holding the club firmly.
Visible crew/equipment: When the hearse crashes down a hill, there's a close-up shot from behind some bushes. In the immediate wide angle, note a distinctive bright white rock which stands out noticeably among the rest of the sandy-colored place, revealing where the previous camera was hidden.
Suggested correction: What exactly is the mistake here? There is no camera or other film equipment visible. There is nothing unusual about the rock. You can see rocks of a similar color in the first picture. Even if you couldn't, a distinctive looking rock on a hillside is far from impossible.
Revealing mistake: When Honey wakes up and walks to grab a dress in the closet, she's supposed to be naked, but one can see a strapless bra covering her right breast.
Continuity mistake: When Bond kills a patrolman on the island, his shirt is dry around his shoulders right after rising out of the water. (01:08:40)
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. (00:48:50)
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 close-up of him screwing on the silencer, his tie disappears. (00:54:40)
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. (00:09:25 - 00:14:05)
Continuity mistake: When Bond goes to Miss Taro's house, as he enters, one of the blinds is turned on the door, but they were all straight before. (00:49:50)
Visible crew/equipment: The camera's shadow is visible on the ground as the car goes off the cliff in the car chase when Bond is headed to Miss Taro's house. (00:48:55)
Continuity mistake: As Bond's driver cuts a hard right turn, the tracks from previous takes are on the road. As the pursuing car draws up to that spot, the dust has quickly settled, and the tracks are suddenly gone. (00:19:05)
Continuity mistake: Near the end when Dr No attacks Bond up on the gantry we see two shots of the radioactivity meter where the red indicator is very close to maximum. The third time we see it just as they tumble off the gantry, it has moved much closer to the danger level. (01:40:00)
Visible crew/equipment: In the first scene, after the "3 blind men" have killed the man, there is a clear reflection of a spotlight on the black car windows, and at least two men visible - a cameraman and what I believe could be director Terence Young. (00:04:05)
Visible crew/equipment: At the airport in Jamaica, when Bond uses the telephone booth, you can see the lighting and crew members reflected in the glass door as he opens it to walk in and out and when Felix opens the door. (00:16:50)
Visible crew/equipment: Just as the blind men assassinate Strangways, One looks towards the camera reflecting a very nice stage light in his sunglasses. (00:04:05)
Continuity mistake: When Dr No, Bond, and Honey are eating dinner, Bond picks up and flexes a table knife. Then there is a wide shot where his hands are under the table. The next tight shot shows him again flexing the knife, then once again goes to the wide angle showing his hands under the table. (01:27:00)
Continuity mistake: When Bond and Honey are looking at the fish for the first time, the position of the fish changes between instant cuts. (01:24:30)
Visible crew/equipment: As Bond gets into the car in Jamaica, a boom is reflected in the paintwork of the car as he says to take him for a drive. (00:18:30)
Continuity mistake: When Mary, Strangway's P.A. is shot, her blood is on a differently patterned carpet than when Bond later on analyses the house. (00:05:00 - 00:22:30)
Continuity mistake: At the end of the movie Bond and Honey are in a small boat when Felix Leiter comes in a bigger boat and gives them a tow. When Bond sits next to Honey he sits on her right hand side. In the next shot he is on her left and in the next shot he is on her right, and back again, etc. (01:44:10)