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.
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: 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.
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.
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: When the stenographer is taking Koskov's account of his escape, there is no paper in the tray and the stenographer isn't pressing the keys. Minutes later the agent/milkman enters and removes paper from the machine.
Continuity mistake: In the teaser, there is something wrong with the landing of the second agent. He lands on a dirt road and runs to his left behind some bushes while pulling his parachute towards the ground. To his right is a rock wall. In the next shot he lands again - presumably below that rock wall. But he was running in the opposite direction. If he changed direction and jumped over the wall to the right he would have run into his parachute. And it can't be a wall behind the bushes to the left he jumped over, because you can see from the shadows that the sun comes from the low side of the wall in both shots.
Continuity mistake: 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.