Plot hole: Necros had absolutely no way of knowing that Bond and Saunders had arranged to meet at the cafe when they did, and wouldn't have had anywhere near enough time to track them down and set up his elaborate booby trap. Saunders only suggested the meeting place and time a few hours earlier, and it was kept strictly between him and Bond. The scene in Tangier where Whittaker tells Necros to kill another British agent takes place on the same day Bond arrived in Vienna; meaning that Necros got from Tangier to Vienna (a 5 hour-plus flight), tracked down Saunders, acquired the materials to booby trap the cafe doors (or had planned this ahead of time - unlikely) and set the trap up well in advance of he and Bond getting to the fairground. There was nowhere near enough time for all of that to happen without Necros having psychic knowledge of Saunders' movements.
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: 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: 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: 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.
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 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.
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.
Continuity mistake: The wheel that is shot off of Bonds car during the frozen lake chase scene is back on the car seconds later as Bond is jumping over the Russian/Czech soldiers.
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 the woman is trying to drive the Jeep into the plane on the runway, in the close up shots there is a shiny steel ramp which we see the car wheels drive up. In the internal and longer shots, we can see that the door looks nothing like this and actually is a sort of lattice, and it has a ridge on it meaning it would be very difficult for the car to drive up.
Continuity mistake: In the opening scene before the credits, 3 MI6 agents parachute out of a plane and into a stronghold. The assassin is already in the stronghold. One agent lands in a sandy area and climbs up a cliff, one lands in a tree and is shot by a guard and the other lands somewhere else. In the next shot of one agent climbing the cliff at the top you can see the assassin hiding a parachute. He wouldn't need to hide a parachute as he didn't have one himself and no agents landed in this area.