Factual error: While Bond and Franks are fighting in the lift you can hear glass breaking, but when Franks picks up a shard of it to stab Bond you can see it's really a piece of Plexiglass. When Franks is forced to let go of the shard his hand shows no cuts or blood, which would have been unavoidable the way he had been holding it.
Factual error: The first laser beam was not generated via a diamond, as Willard Whyte says. The first functional laser device, which was constructed by Theodore Maiman, used a ruby rod.
Factual error: In Blofeld's offshore control room there's an Earth-globe turning under a model of the satellite, to illustrate its orbital groundtrack. The way it's arranged, however, shows an orbit which is impossible. It shows the satellite tracing a groundtrack over a constant latitude. The only instance in which this is possible is if the orbit is directly over the Equator, whereas the model shows it over a latitude well within the Northern Hemisphere.
Factual error: When Bond is inside the oil rig, the shots switch from the satellite control room to the satellite itself orbiting. When the satellite fires at the underground missile, it's orbit direction reverses. Then, when it fires at the Russian sub and the Chinese military base, it stops before it fires. This is impossible, as Newtons 3rd law states that for every action there is an equal and opposite reaction. For the satellite to reverse or stop, boosters would be needed at the front of the satellite (of which there aren't any) to counter it's speed. And even if they were there, the direction change and stop wouldn't be as sharp as the movie shows.
Factual error: When Mr. Wint and Mr. Kid assassinate the doctor in the South African desert, they use a scorpion. Scorpions are poisonous, but the sting is more like a bee's, and woudn't kill a healthy adult.
Factual error: The satellite uses a laser as its weapon, which can be only as powerful as its root energy source. It obviously doesn't have a nuclear reactor large enough to yield that much power, and it can't be solar power, since the collecting area of the dish is orders of magnitude too small to provide power at a level sufficient to lay waste to whole submarines and missile installations.
Factual error: When the submarine blows up under water the explosion we see shows no water being thrown up.
Factual error: Diamonds, being pure carbon, would burn in the cremation of the body containing them. Cremation temperature is about 1,000 degrees Celsius, diamonds burn at about 850.