Factual error: During the boat chase scene, Bond throws a grappling hook/anchor from the old boat he is driving onto the deck of the rubber boat "riding" his. The rubber boat is then violently yanked off of Bond's boat and crashes. This makes no sense. For the rubber boat to be yanked off that way, the other end of the anchor line would have to be tied to something stationary. However, the other end of the line is just lying in Bond's boat. There's even a shot of it sitting there.
Continuity mistake: When Bond is talking to Mathis at a table at the cottage in Italy, pay attention to the watch on Mathis' wrist. First it faces the side of his wrist because that way it is best shown on screen, but in the next shot, still at the table, it suddenly faces the outside of his wrist like watches are usually worn.
Continuity mistake: When Bond is on the plane with Mathis, and asks the waiter for his usual drink, between shots, Mathis' hair changes - in some shots there's a lock of hair on his left down by his eye, in some shots he's got two bits of hair loose on his right, and in others his hair's all in place. All this without him ever touching it.
Continuity mistake: While Greene is talking to his associates in Bregenz, the opera is approaching the end of act one which finishes just as Greene and Bond meet in the hall. However, at this point Mario Cavaradossi is suddenly being shot, which is the end of act three/the end of the opera. At the same time the music jumps to the end of act two, just after Tosca stabbed Scarpia; this scene is then shown while Bond is being chased.
Continuity mistake: During the fight scene at the Hotel Dessalines with Slate, Bond and Slate go through glass pane doors and land on the terrace, and Bond kills Slate. Notice that at first there is a broken piece of wood pane laying next to Slate's head; the next shot shows no wood pane, and there is a door knob that wasn't laying close to Slate's head in the first shot.