Factual error: During the war games they have Jefferson pose as a major in order to facilitate the commandeering of the ambulance and the jeep. Regardless of their personal feelings in the matter the ambulance crew and the driver and troops in the jeep would be perfectly aware that no black man would ever be promoted to a position of authority in an otherwise all white command. We may find it repugnant today but the US Army was rigidly segregated during World War 2 - and it stayed that way until 1948. Jefferson may have been inducted into a special unit like the Dirty Dozen but considering that the future of the entire mission is riding on their success at the games, throwing it all away like that makes no sense at all.
Factual error: Two rocket lift-offs are shown. For the American lift-off, they show an Atlas-Agena (American) rocket booster but for the Soviet lift-off, they show a Gemini-Titan (also American) rocket booster. Compounding the mixup is that the film's Jupiter capsules are basically just Gemini craft, which are seen atop what the film presents as the Russian rocket.
Factual error: When M and his entourage arrive at Bond's estate, their cars are surrounded by sheep. They then drive on down an unsurfaced road to Bond's house, past a pride of lions he keeps on the grounds. A series of sweeping overhead shots shows us that it is all one huge field, with no fences or the like. Those sheep aren't going to last very long.
Factual error: When Bonnie and Clyde are killed he is lying on the ground in front of the car, and she is in the driver seat. In real life they were both killed in the car. He was in the driver seat, and she was lying up against him. (01:44:20)