Factual error: Austria is famous for its mountains and ski resorts. But certain parts of Austria are quite flat. And the border region between Bratislava and Vienna is VERY flat. No chance to cross the border over a mountain with a ski resort like shown in the movie, unless you take a 600km detour with three more border crossings.
Factual error: When the police car Bond has lasered through splits in half, the metal on either side of the wheels has been cleanly cut but the wheels themselves are undamaged, despite the fact that Bond never switched it off.
Factual error: In the "Soviet" base in Afghanistan, every equipment, from armoured carriers to light tanks, are of French manufactured. And the transport plane is American C-130 Hercules.
Continuity mistake: At the beginning, Bond sees the bad guy get into a truck and drive off - he chases after him, about 20m behind. They're travelling on parallel roads, Bond running, and the bad guy driving (quite fast), but when Bond's road runs out he manages to jump on top of the truck, having miraculously caught up with him.
Continuity mistake: Gen. Koskov is flown out of the Vienna gas reservoir in an RAF Harrier. Austria is a neutral country, and no foreign military aircraft are allowed to enter Austrian airspace. OK, perhaps it was a secret mission. But it would not have been secret for a long time. The Harrier is not really a silent plane and there are people living around the reservoirs - and the center of Austrian air control is about 3 km away from the reservoirs.
Factual error: The Bratislava Academy of Music which is shown in the movie, is in reality the Vienna People's Opera.
Plot hole: When his plane runs out of fuel, Bond and Cara eject in the jeep. When the jeep ejects, the plane is just a couple meters off the ground. Cut to a shot of the plane crashing into a cliff, it's at least 10 to 20 meters up. Impossible for the plane to have gained altitude; the engines were off and no updraft of air would be strong enough to lift a plane that size.
Other mistake: When James is on the top of the jeep, there is a brief shot of it from behind as they go past an armed soldier. Watch carefully, the jeep goes over a few bumps and Bond on top seems to jump all over the place in a very unnatural way. This is because the footage has been sped up to make the Jeep appear to be going faster.
Continuity mistake: Bond drives not one, but two completely different Aston Martins in "The Living Daylights." When he drives up to the safe house early in the movie, he's driving an Aston Martin V8 Volante (actually the 'personal' car of then Aston Martin chairman Victor Gauntlett, and loaned by him to the Bond producers). But the "stunt" Aston Martin - used by Bond to escape from Bratislavan Police and Army - is a V8 Oscar India Coupe. Yet both cars have the same licence plate (B549WUU). There's also a scene in Q's workshop where the technicians are "winterising" the Aston Martin, in an attempt to disguise the difference.
Audio problem: In the sniper scene, Bond is asked if he wishes to use the soft-nosed bullets to kill the potential assassin to which he replies, 'No the steel-tipped'. There isn't any lip movement, however, after the word 'no'.
Continuity mistake: When the bad guy falls to his death from the plane after the fight with Bond, in one shot you can see the plane is a two-engine one, not the four-engine Hercules it's supposed to be. According to the DVD commentary, the plane was used due to the high cost of using the Hercules.
Continuity mistake: When Bond and Necros are fighting on the opium packages behind the plane, in the wide shot we see that Bond is all the way at the top of the bundle of packages - he takes his knife and cuts the net near his knee. In the next wide shot we see that Bond's head is above the top of the bundle of packages, but in the next close-up, packages are dropping from above Bond's head.