Continuity mistake: When JB is driving the white truck and is being bombed with grenades from the helicopter the truck gets smoke blackened, but when he arrives at the speedboat all the smoke marks have gone.
Continuity mistake: The train is stopped because Spectre has pushed a 1950's style Dodge truck full of flowers in the trains path. Later, when James is driving it trying to avoid the grenades dropped from a helicopter, the truck has turned into a very different looking 1961 Chevrolet truck.
Continuity mistake: When Bond and Tatiana are in the boat chase and are being followed, they drop four cans of fuel in the sea. When Bond blows them up, there are way more than four fuel explosions in the sea.
Visible crew/equipment: In the scene where James Bond shoots down the helicopter then it crashes, he emerges from the rocks to run from the crash site to the right of picture, just as you see Sean Connery emerge from behind rocks from the right in the same scene. So for a about a second there are two James Bonds in picture. One is the stunt man and the other is Sean Connery.
Other mistake: When James Bond's friend Kerim Bey gets shot at the gypsy camp, look closely, he is rubbing fake blood into his own arm.
Continuity mistake: Just after Grant has hit 007 on the back of his head and knocked him out, Grant searches through the pockets of 007, he takes out some money and puts it into his lower left side pocket. But when 007 kills Grant and searches his pockets, 007 takes back the money from Grant's inside top right hand pocket.
Continuity mistake: James Bond is chased by an helicopter. When seen from above, Bond carries an attaché case in one hand; when shown from the ground, the case is in the other hand. This change happens many times, as the camera point of view switches.
Continuity mistake: When Kerim Bey is making a sniper shot towards a billboard with the rifle being steadied on Bond's shoulder, check out Bond's eyebrows - they are long in one shot, short in another....obviously painted on.