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.
Continuity mistake: When Bond has his final confrontation with Whitaker, he empties his PPK at him in an attempt to take him down. In the process, he hits the gunshield on Whitaker's weapon five times, and it remains clean. But when Whitaker rounds the corner a few seconds later, the impacts from the PPK bullets are suddenly visible on the shield's surface.
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.
Continuity mistake: When the plane crashes at the end all four engines are running at high speed, but before that all four engines had stopped because they ran out of fuel.
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 Bond and Milova escape Bratislava it is snowy and wintry. When they arrive in Vienna, which is only 50 miles away and at the same latitude, it is late summer or early autumn, with signs of leaves changing.
Audio problem: When Saunders says "In the box, between the KGB minders" at the concert, his mouth is not moving.
Factual error: When Bond steals the opium laden plane from the airbase, Kamran Shah and his men are busy fighting the Russians. Considerable flying time later (during which Necros gets the boot), Bond then drops the bomb on the bridge. Somehow Kamran has managed to get ahead of the plane on horseback.
Continuity mistake: When Bond exits the tunnel in the Aston Martin they get fired upon by an armoured car - look at the scenery outside the Aston, from inside there is no left turn, but one appears out of nowhere for Bond to take and head down to the frozen lake.
Factual error: Aircraft have multiple independent tanks. If one tank is hit, it should be able to fly for hours on the others. It would be very unlikely that all tanks of the plane got hit during the firefight - some are in quite well-protected spots. It is actually very nigh impossible to pierce every single tank from the outside and still have a flyable plane remaining.