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.
Continuity mistake: When Blofeld is just about to shoot Bond with a Webley & Scott Mk. IV revolver in .455 Webley caliber, Blofeld's hand is hit with a ninja throwing star. However, the gun he drops isn't the Webley, but a Smith & Wesson .38 Special.
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.
Plot hole: Towards the end of the film when Newman and the remaining stagecoach people are in the cabin at the top of the hill, Richard Boone's character sends one of his two henchman (the Anglo, not the Mexican) around to the back of the cabin to apparently surprise them from behind. Then Newman's character walks down the hill and Boone and the Mexican henchman are all killed in a shootout. Everyone comes out of the cabin, comes down the hill and the credits roll. I guess that now, almost 40 years later, that poor Anglo-henchman is still behind the cabin, waiting for them to come out.
Revealing mistake: When the farmer is going to shoot the sign the bank put up, you can very well see the mark where the hole is going to appear.
Other mistake: The villain's plan is to impersonate along with his large crew a platoon of the Mexican army. He already captured the soldiers and has them incapacitated, all he needs to do is take their uniforms. Instead of doing so, though, he mows down the whole lot with a heavy machinegun. When it's time to put on the show, everyone wears nice and tidy white uniforms.