Continuity mistake: When Tracy is battling that balding guard during the climax, she finishes him off by pulling him into a metal patterned wall in a way that ends up with one of the circular sections on his head like a crown. When he falls down the stairs this circular section disappears.
Plot hole: Blofeld is played by Telly Savalas. In a previous film, Blofeld had met James Bond and had ordered him killed, yet in OHMSS, when Blofeld meets James Bond, he doesn't recognise him. It's well established over the course of the Bond movies until the reboot with Casino Royale that they all take place in one timeframe, so they should have recognised each other.
Other mistake: In the scene when the helicopters arrive over the research center, look at the heli in the bottom right - it just fades out, while one on the left materialises, and the one in the middle changes position. Notice that after all the helicopters have changed place, you can see the helicopter that faded out appear on the helipad
Continuity mistake: At the start of the scene where Bond is helping with the assault on Piz Gloria, look at Tracy's hand just after the bald guard presses it down on the object to disarm her. You can see blood, but a couple of minutes later when she kills him there is no blood to be seen.
xx:xx:xxMr A Mclelland
Continuity mistake: In the stock car race scene, when Bond and Tracy first drive onto the track the number 11 red car spins out to avoid a collision and ends up facing against the wrong way. Two seconds later we see the number 11 car backing up so as to face the correct direction. Two seconds after that, in a long shot, we see the number 11 car going forward again. A few seconds later we see the number 11 car facing the wrong direction as it begins backing up again. Several seconds latter, the Mercedes containing Blofeld's henchmen enters the track and once again the number 11 car is stopped facing the wrong direction. Later in the scene the Mercedes collides with the number 11 car causing it to spin out and end up facing the wrong direction, yet a few seconds later we see the number 11 car racing along in the correct direction as Bond and Tracy pass it.
Factual error: Of all the characters, major and minor, who ever speak German in Switzerland, not one speaks Swiss German. The accents are very different (Swiss German can be almost incomprehensible to speakers of High German), and there's also different vocabulary. While some of the characters might just be non-Swiss speakers of German, at least the underlings at Piz Gloria should be speaking Schwyzerdeutsch.
Continuity mistake: In the car chase in Switzerland Bond and Tracy are being chased by Blofelds men, and at one point the Mercedes with the bad guys swerves off the road. But in the inside shots of Bond and Tracy's Cougar you still see the Mercedes' headlights, still on the road, in the rear window.
Continuity mistake: When Tracy and Bond are talking in the casino, and Bond tells her to stay on 5, she has her left hand resting against her chin. As she says "people who want to stay alive play it safe" she moves her hand down to the table, but then when the camera cuts back to Bond the reverse shot of her shows her hand still by her chin, and then she moves it down again.
Continuity mistake: In the scene where Bond is getting out of Draco's car to visit Gumbold, his tie is neatly within his jacket. He bends over to speak to Draco, and the tie is dangling out of his jacket. In the next shot, he straightens up, and the tie is once again neatly within his jacket.
Plot hole: Blofeld tells Bond that he realised he was not the real Sir Hilary Bray when Bond told him that the Bleuchamp tombs are in the Augsburg Cathedral. Blofeld informs Bond that they are in-fact in the Saint Anna Kirche, and the real Sir Hilary Bray would've known this. However Bond had gotten his information about the Bleuchamp tombs in Augsburg from the real Sir Hilary Bray earlier in the film.
Continuity mistake: When Bond and Che are fighting, Che knocks out one of the white wooden bars behind Bond. However, in the next shot, two bars are missing on the upper half of the wooden structure, one on the bottom half. Seconds later, just before Bond throws Che into it, the bottom half of the structure is complete again, and only one bar is missing on the upper half.
Other mistake: In the bobsled chase, Blofeld arms a grenade, which drops to the floor of his sled, where it rolls around with every turn. He arms and throws a second grenade onto the track, where it is detonated by Bond's sled. The original armed grenade loose in Blofeld's sled never detonates, even when that sled crashes.
Other mistake: As the assault on Piz Gloria begins and the helicopters approach the facility, on the right of the screen one seems to be hovering near the helipad as another passes behind it. The helicopter in front fades to a slightly different position as the one passing it disappears and reappears several meters ahead. On the left of the screen the third helicopter appears out of thin air. (This was obviously caused by a dissolve effect, but since the sound effects are constant there doesn't seem to be any indication that a visible edit or time shift was intended for this scene, so it's a mistake).